Question

Suppose that the IQs of university​ A's students can be described by a normal model with mean 150150 and standard deviation 77 points. Also suppose that IQs of students from university B can be described by a normal model with mean 120120 and standard deviation 1010. ​a) Select a student at random from university A. Find the probability that the​ student's IQ is at least 140140 points.

Answer 1

The probability that the​ student's IQ is at least 140 points is of 55.17%.

Explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

University A:
`\mu = 150, \sigma = 77`

a) Select a student at random from university A. Find the probability that the​ student's IQ is at least 140 points.

This is 1 subtracted by the pvalue of Z when X = 140. So

`Z = (X - \mu)/(\sigma)`

`Z = (140 - 150)/(77)`

`Z = -0.13`

`Z = -0.13` has a pvalue of 0.4483.

1 - 0.4483 = 0.5517

The probability that the​ student's IQ is at least 140 points is of 55.17%.