Question

1.) Suppose the scores on the Braver Pure Intelligence Test (BPIT) are normally distributed with a mean of 200, and a standard deviation of 20. If we pick someone from the population at random and give him or her the test, the probability that this person’s BPIT score will be over 225 is approximately…

.106

.274

.302

.455

.599

None of the above

2.) The heights of American men are normally distributed with a mean height of 70 inches, and a standard deviation of 3 inches.

If we measure the heights of 4 randomly chosen American men, the probability that their mean height exceeds 71 inches is...

.02

.07

.09

.25

.37

There is not enough information given to answer this question.

3.) (Continued from Question 2)

To be among the tallest 5% of all American men, what is the minimum height that an American man be?

71.64 inches

73.84 inches

74.12 inches

74.92 inches

76.99 inches

Answer 1

1)

Let X denote the scores on the Braver Pure Intelligence Test (BPIT)

= 200 (mean)

= 20 (standard deviation)

Here we have to find P(X>225)

=> P(X>225)

As X follows normal so, will follow standard normal. Here Z is the standard normal variable

  (we get the value from z table)

Answer: 0.106

2)

Let X denote the heights of American men

= 70 (mean)

= 3 (standard deviation)

n = 4 (sample size)

Let be the sample mean

Here we have to find P(>71)

As X follows normal so, will follow standard normal. Here Z is the standard normal variable

  (we get the value from z table)

Answer: 0.25

3)

Let X denote the heights of American men

= 70 (mean)

= 3 (standard deviation)

Let c be the minimum height required to be among the tallest 5% of all American men

5% means in probability 5%/100%=0.05

So here to find c we use the equation

=> P(X< c) = 1 - 0.05

As X follows normal so, will follow standard normal. Here Z is the standard normal variable

From z-table we get

Answer: 74.92 inches