Mensa Membership in Mensa requires a score in the top 2% on a ...

Question

Mensa Membership in Mensa requires a score in the top 2% on a standard intelligence test. The Wechsler IQ test is designed for a mean of 100 and a standard deviation of 15, and scores are normally distributed.

a. Find the minimum Wechsler IQ test score that satisfies the Mensa requirement.

a. Find the minimum Wechsler IQ test score that satisfies the Mensa requirement.

Accepted Answer

Hi, everyone, let's take a look at this practice problem. This problem says a certain job position requires applicants to be in the top 10% based on their scores from a professional aptitude test. The test is designed with a mean score of 300 and a standard deviation of 50. Determine the minimum score an applicant must achieve to meet this requirement. We're given 4 possible choices as our answers. For choice A, we have 236. For choice B, we have 364. For choice C, we have 312, and for choice D, we have 346. So for this question, we need to determine the minimum score an applicant must achieve in order to be in the top 10%. So instead of working with the raw score, we're actually going to begin by looking at the Z score that corresponds to the top 10%, because it's going to be easier to find, and then to use that Z score to find the raw score on the test that we need to achieve. So, in order to be in the top 10%, we need the probability. Of capital Z. is greater than or equal to lowercase c, and that's going to be equal to 0.10. So here, I've just taken 10% and converted it from a percentage to a decimal point. That's where the 0.10 comes from. Now, this here is equivalent to the probability. Of finding capital Z is less than or equal to lowercase z, which is going to be equal to 0.90. So that second probability is going to be a little bit easier to use if we're using a standard normal distribution table to find our Z value. So, either using a table or a calculator, we can find that the Z value is going to be equal to. 1.28, so we will have Z equal to 1.28. So now what we need to do is to convert the Z score into a raw score. So, recall that our raw score, which we'll label as X, is going to be equal to you. Plus, Z multiplied by sigma. Where mu here is our mean and sigma is the standard deviation, and we were given both of those quantities in the problem. So this is going to be equal to, for our mean, we have 300. Then we'll have plus, 1.28, multiplied by our standard deviation, which we're given from as 50. And when we evaluate this expression, this is going to be equal to 364. So that is the score that we're looking for for this problem. And if we compare our answer to our answer choices, we see that the correct answer choice corresponds to answer choice B. So I hope that this explanation has been useful, and I'll see you in the next video.

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