Question

The length of time needed to complete a certain test is normally distributed with mean 60 minutes and standard deviation 10 minutes. (a) What is the relative frequency of people who take between 45 and 65 minutes to conlplete the test? Sketch a standard normal curve and shade the area in question.

Answer 1

Answer:

0.6247

Step-by-step explanation:

In order to find the frequency of people who complete the test between 45 and 65 minutes, we have to find z

Z = (x – mean)/standard deviation

Le x be the time to complete the test

Z1 = (45 – 60)/10 = -1.5

Z2 = (65 – 60)/10 =  0.5

Then we use the z table to find the area under the curve.

Area for Z1 = 0.4332

Area for Z2 = 0.1915

The relative frequency is the area between the two z-scores:

0.4332 +0.1915 = 0.6247

Graphic with shaded area is attached

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