Applied and Computational Questions A traffic study at one point on an interstat

Question

Applied and Computational Questions

A traffic study at one point on an interstate highway shows that vehicle speeds are normally distributed with a mean of 61.3 mph and a standard deviation of 3.3 mph. If a vehicle is randomly checked, find the probability that its speed is between 55.0 mph and 60.0 mph.

            ANSWER:

Two-year college students have mathematics competency scores that are normally distributed with a mean of 35 (the maximum possible score is 48). The 90th percentile is 40. Find the standard deviation of the math competency scores.

            ANSWER:

Scores on a computer science aptitude test are normally distributed. The standard deviation of the distribution is 6.0, and the 95th percentile for the test is 92. Find the mean score for this test.

            ANSWER:

Explanation / Answer

= 61.3, = 3.3

z = (x - )/

z1 = (55 - 61.3)/3.3 = -1.9091

z2 = (60 - 61.3)/3.3 = -0.3939

P(55 < x < 60) = P(-1.9091 < z < -0.3939) = 0.3187

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