Which of the following statements is are true regarding the normal distribution curve *?

On the 3rd of March 2020, I stopped posting daily lessons on this blog and I began working on a new website. The new site is called ielts-simon.study and I now publish my daily lessons there.

Free email list:

As well as the member website, I also have a free email list for non-members. You can join it by filling in this form. You'll receive an email from me approximately once a week.

This blog:

Although I'm no longer updating it, this blog is still alive and it contains a few thousand IELTS lessons. Have a look around and I'm sure you'll find some advice, language or exam practice that helps you to improve.

Today I'm making a difficult decision: I'm taking a break from this blog for a while.

There are over 2800 lessons here on the blog, so there's plenty for you to read. My other IELTS resources are also still available.

Read the following text and try the quick exercise below it.

Primal Therapy

Primal therapy is a trauma-based psychotherapy created by Arthur Janov, who argues that neurosis is caused by the repressed pain of childhood trauma. According to Janov, repressed pain can be sequentially brought to conscious awareness for resolution through re-experiencing specific incidents and fully expressing the resulting pain during therapy. In therapy, the patient recalls and reenacts a particularly disturbing past experience, usually from early in life, and expresses normally repressed anger or frustration, especially through spontaneous and unrestrained screams, hysteria or violence. Janov criticises the talking therapies as they deal primarily with the cerebral cortex and higher-reasoning areas and do not access the source of emotional pain within the more basic parts of the central nervous system.

Primal therapy became very influential during a brief period in the early 1970s, after the publication of Janov's first book, The Primal Scream. It inspired hundreds of spin-off clinics worldwide and served as an inspiration for many popular cultural icons. Singer-songwriter John Lennon and actor James Earl Jones were prominent advocates of primal therapy. However, it has since declined in popularity, partly because Janov did not produce enough evidence to convince research-oriented psychotherapists of its effectiveness.

Are the following statements true, false or not given?

  1. During primal therapy sessions, patients are encouraged to remember traumatic childhood events.
  2. Primal therapy patients must talk calmly to the therapist.
  3. Primal therapy enjoyed a short heyday.
  4. Although it is less popular these days, many people still advocate this form of therapy.

As I'm sure you know, we normally place the adjective in front of the noun in English e.g. "the red car" instead of "the car red".

However, English is a crazy language, and rules are there to be broken!

If you read yesterday's lesson (and clicked on this link), you may have seen the following examples of noun + adjective:

  • someone important
  • somewhere nice
  • the best room available
  • the only decision possible
  • the worst choice imaginable
  • the person responsible

Remember: The 'rules' that you find in an intermediate (or even 'advanced') grammar book are probably a simplification. There are deeper levels to be discovered!

There was an interesting discussion in the comments below Wednesday's lesson about the phrase "I can buy any product imaginable".

Here's a summary of the questions in that discussion:

1) Why did I write any product imaginable instead of any imaginable product?
2) Would any imaginable product also be correct?
3) Is there a difference in meaning between the two phrases?

I'll try to answer without going deep into grammar, but if you really like the grammar side of things, have a look at this page (especially the part about 'the only decision possible' and 'the worst choice imaginable').

  1. The simple answer is that "any product imaginable" sounds better to me as a native speaker. This phrase isn't my own original creation; I've probably heard or read it many times in similar contexts, so it's the instinctive phrase to use.
    Note: There are 14,300 Google search results for this collocation.
  2. While "any imaginable product" is also grammatically correct, it seems just a little less natural to me. The emphasis is slightly different, and the meaning could also be understood in a slightly different way.
    Note: There are only 905 Google search results for this collocation.
  3. This is debatable. If I had to give you my view, I would say that an "imaginable product" could include products that don't currently exist (e.g. a flying car), whereas my phrase "any product imaginable" tends to refer to products that currently exist.

In the end, the Google results and my instinct as a native speaker are probably your best guide. In normal English usage, "any product imaginable" is the typical collocation.

Let's look at a new speaking topic:

Describe a day out that you enjoyed recently. You should say

- where you went
- whom you went with
- what you did that day
- and why you enjoyed the day out.

Note: When we talk about a "day out", it means that you went somewhere for leisure purposes. I wouldn't talk about anything related to work or studies here.

I was reading The Economist yesterday, and I noticed these sentences:

America's total student debt, at over $1.5trn, is larger than the national borrowing of most countries. It has quintupled in size since 2004, overtaking both borrowing on credit cards and car finance.

I've highlighted a few useful features in the two sentences:

  1. adding a statistic between two commas using "at"
  2. a comparative: larger than
  3. cohesion (referencing) using the pronoun "it"
  4. quintupled = increased fivefold
  5. overtaking: you may be able to use this word when describing a graph
  6. comparing and contrasting using "both... and..."

If you're reading articles in English, look out for real examples of the types of description that you might use for an IELTS task.

When you have written a plan, you then need to turn your notes into full sentences. Let's try this using the paragraph plan below.

Paragraph plan:

- High street shops are disappearing because of online stores.
- Online shopping is faster, cheaper and more convenient.
- People can sit at home, search for deals, receive delivery the next day.
- It is impossible for normal stores to compete with the range of choice.
- Personal example: recent purchases on Amazon.

Full paragraph:

In my opinion, high street shops are disappearing due to competition from online shopping websites, which are cheaper and more convenient. Web-based stores allow customers to search for the best deals, make purchases from the comfort of their homes, and receive delivery of their purchased items the next day. Furthermore, it is impossible for traditional bricks-and-mortar stores to compete with the range of choice that can be found online. For example, I recently used the website Amazon to buy some fairly rare academic textbooks that were not stocked at my local bookshop. As a customer, the fact that I can find any product imaginable online makes it almost pointless for me to make a trip to my local high street.

Have you seen the video lesson that I published here a few years ago?

Check it out and feel free to ask any questions about the lesson in the comments area below.

The following excerpt comes from test 3 in Cambridge IELTS book 10.

The travel industry includes: hotels, motels and other types of accommodation; restaurants and other food services; transportation services and facilities; amusements, attractions and other leisure facilities; gift shops and a large number of other enterprises. Since many of these businesses also serve local residents, the impact of spending by visitors can easily be overlooked or underestimated. In addition, Meis (1992) points out that the tourism industry involves concepts that have remained amorphous to both analysts and decision makers. Moreover, in all nations this problem has made it difficult for the industry to develop any type of reliable or credible tourism information base in order to estimate the contribution it makes to regional, national and global economies.

Are the two statements below true, false, or not given?

  1. Visitor spending is always greater than the spending of residents in tourist areas.
  2. It is easy to show statistically how tourism affects individual economies.

Extra task:
Can you explain the meaning of the phrase "the tourism industry involves concepts that have remained amorphous to both analysts and decision makers"?

I often hear from students who are disappointed because their scores have only improved by half a band. For example: "I've been studying for 3 months but my score has only improved by 0.5".

My reply is always this: You should be happy! An improvement of half a band is great, and it shows that you are on the right track.

Remember: small, gradual improvements are signposts on the path to success!

All students learn to link ideas using words like "however", "furthermore" etc. Most students don't realise that the word "this" is also a linking word. Look at the following examples:

  • Nowadays, people can use the Internet to work from home. In this way, people who do not have access to transport can find employment.
  • Most products are built to last only a short time, and this creates a "throw-away" culture.
  • A global economy means free trade between countries. This can strengthen political relationships.

The word "this" refers to the sentence or idea that came before. "This" helps you to link ideas and avoid repetition. Native speakers and good writers use "this" a lot, and the IELTS examiner will be impressed if you can use it.

An IELTS teacher asked me the following questions:

Is it compulsory for candidates to address all of the prompts on the cue card? What happens if candidates ignore the prompts but speak well about the topic anyway? And what happens if the candidate misunderstands the question and speaks about a different topic?

Here are the answers that I gave the teacher:

I tell my students to use the prompts because they help you to structure your answer. However, it is still possible to get a very high score even if you don't address all of the points e.g. if you speak well about the topic but miss the last point or two. I don't recommend ignoring the points completely, because there's a danger that you'll go off task if you do that.

If you misunderstand the question and give an unrelated answer, I'm afraid you'll get a very low score. The reason is that candidates could memorise a perfect answer if off-topic answers were allowed.

Fill the gaps in the following text using the words below it. If you find any of the gaps difficult, miss them and come back to them after doing the easier ones.

Emigration from the UK

The number of people leaving the UK for 12 months or more ______ ______ record ______ in 2008, ______ an estimated 427,000 people emigrating. This ______ ______ from 341,000 in 2007.

There has been a large ______ ______ the number of people emigrating for work related reasons, particularly those with a definite job to go to. In 2008 an estimated 136,000 people emigrated from the UK to take up a definite job, ______ ______ 100,000 in 2007.

- in
- high
- increase
- up
- reached
- with (x2)
- a
- compared
- was

There are three things that you need to think about when planning an essay:

  1. How you will answer the question (your position / opinion)
  2. How you will structure your essay to communicate your answer
  3. The ideas that you will include in your main paragraphs

For example, let's do an essay plan for the question below.

Many high street shops have gone out of business in recent years. Why do you think this has happened? Is it a positive or negative development?

1. My answer

Online shopping is the main reason. The trend is both positive and negative.

2. Structure: four paragraphs

- Introduce the topic, and give a brief answer to both questions
- Main paragraph about online shopping
- Main paragraph about the positive and negative impacts
- Conclude by summarising the overall answer

3. Ideas for the main paragraphs

  • Online shopping is faster, cheaper and more convenient. People can sit at home, search for the best deal, pay, and receive a delivery the next day. Impossible for stores to compete. Personal example: recent purchases on Amazon.
  • Positives: a world of choice, a solution for busy people or those who can't leave the house. Negatives: rising unemployment, loss of community as high streets become deserted.

It's a good idea to do practice tests (e.g. using the Cambridge IELTS books) in preparation for the listening exam. Here's some advice to help you benefit from doing practice tests:

1. Your score is not the most important thing
The important thing is what you have learnt by doing the test. Were there any new words or phrases that you can learn? What did you find difficult? Did any of the questions trick you? In other words, what do you need to do to improve your score?

2. Check how accurate your answers are
Be strict with yourself; every grammar or spelling mistake is important. For example, if the speaker says "The library has a collection of newspapers", you must not write "collection of newspaper".

3. Get into the habit of moving on
If you missed something, forget about it and move on. Always prepare for the next question rather than worrying about a previous question. When you are given 30 seconds to check your answers, use the time to look at the next section instead.

Let's look at some examples of paraphrasing, using the text below.

What is an 'elevator pitch'?

An “elevator pitch” is an overview of a product, service, person, group, organisation or project, and is often part of a fund-raising, marketing, brand or public relations program. The name "elevator pitch" reflects the idea that it should be possible to deliver a short but effective presentation in the time span of an elevator ride from the ground floor to the directors’ boardroom on the top floor of a building.

An elevator pitch is often used by an entrepreneur pitching an idea to an investor to receive funding. Venture capitalists often ask entrepreneurs to give an elevator pitch in order to quickly weed out bad ideas and weak teams. Other uses include job interviewing, dating and professional services. Proposals for books, screenplays, blogs and other forms of publishing are often delivered via an elevator pitch, which may be presented in oral, written or video formats.

Which words or phrases in the passage are similar to those below?

  1. a summary
  2. succinct
  3. gain financial backing
  4. eliminate
  5. spoken

The best kind of testimonial (positive feedback) is when a student tells me that he or she has passed the IELTS test and no longer needs my help.

For example, here's a message that I received earlier today from someone who unsubscribed from my member site:

"It is a wonderful resource, Simon. I have to leave the membership as I cleared* my Academic IELTS and got the required scores. Thank you for all the support!"

*Instead of saying "I cleared", it would be better to say "I passed the IELTS test".

I studied French at school for seven years, and my teachers helped me to accumulate quite a lot of knowledge about the language.

However, when I visited France I still felt like a beginner. I found it difficult to understand native speakers, and I couldn't speak naturally; I had to construct sentences in my head before I spoke, and I was constantly worried about making mistakes. In short, I had knowledge but not much skill.

Do you feel like this when you speak or write in English? Maybe it's time to stop studying English and start practising it as much as possible!

Look at the following question and my sample answer, in which I've highlighted the adjectives.

What do you think are the characteristics of a good speaker?

I think good speakers are confident and passionate about the subject of their speech. They need to be interesting and engaging. I think a speaker's body language is also really important. A famous example of a great speaker is Barack Obama; he seems to be a naturally inspiring speaker, but I'm sure that practice and preparation are more important than natural talent.

Note:
Can you see how the adjectives bring my answer to life?

You probably know how to describe a 'double' increase. For example:

  • The number of x doubled.
  • There was a twofold increase in x.

But how do we express the opposite e.g. a decrease from 10 to 5?

Which of the following statements are true regarding normal distribution curve?

Check all that apply: The graph of the Normal Distribution is bell-shaped, with tapering tails that never actually touch the horizontal axis_ The mean, median and mode are all equal and occur at the center of the distribution.

Which of the following statement is correct for normal distribution?

the only TRUE statement is the 1st statement, ie. "The normal distribution is single peaked and symmetric".

What is true about a normal distribution?

Normal distributions are symmetric around their mean. The mean, median, and mode of a normal distribution are equal. The area under the normal curve is equal to 1.0. Normal distributions are denser in the center and less dense in the tails.

Which of the following statement is true about normal probability distribution?

Answer and Explanation: The normal probability distribution has a mean and standard deviation as its parameters. It's mean is 0 and the standard deviation is 1 only when the normal distribution has been standardized, otherwise, it can take on any values. The normal probability distribution is symmetrical.