Question

The average time it takes college freshmen to complete the Mason Basic Reasoning Test is 38.3 minutes. The standard deviation is 3.2 minutes. Assume the variable is normally distributed.
Find the probability that it will take a student less than 30 minutes or more than 45 minutes to complete the test.

I REALLY NEED HELP :(

Answer 1

The first step is to find the z-score for 30 minutes using the formula
\[z=\frac{X-\mu}{\sigma}=\frac{30-38.3}{3.2}=can\ you\ calculate?\]

Answer 2

-2.95

Answer 3

Not quite. It is -2.59. Now use a standard normal distribution table to find the cumulative probability for a z-score of -2.59. A suitable table is at the following link. Click on 'normal.pdf'.

Answer 4

.0048

Answer 5

http://www.math.bgu.ac.il/~ngur/Teaching/probability/

Answer 6

Correct! Good work. Can you find the z-score for 45 minutes?

Answer 7

.9817

Answer 8

Good. Now subtract 0.9817 from 1.0000 to find the required probability.

Answer 9

@GLITTERGIRL5575 Are you there?

Answer 10

.0183

Answer 11

Correct! Well done.

Answer 12

@GLITTERGIRL5575 Are you there?

Answer 13

The probability that it will take a student less than 30 minutes or more than 45 minutes to complete the test is found as follows:
\[P(A \cup B)=P(A)+P(B)-P(A \cap B)\]
Required probability = 0.0048 + 0.0183 - (0.0048 * 0.0183)