Question

The average length of time required to complete a jury questionnaire is $40$ minutes, with a standard deviation of $5$ minutes. What is the probability that it will take a prospective juror between $30$ and $50$ minutes to complete the questionnaire?

• A. About $85\%$
• B. About $90\%$
• C. About $95\%$
• D. none

Answer 1

The correct option is C About $95\%$

For normal distribution ,

Average length of time required to complete a jury questionnaire is 4040 minutes

Mean ($\mu$)=40

standard deviation($\sigma$)=5

Probability that it will take 30 to 50 min i.e, P(30<x<50)

For standard normal distribution curve

Z=(x-$\mu$)/$\sigma$

(30-40)/5<(x-$\mu$)/$\sigma$<(50-40)/5

-2<Z<2

For standard normal distribution mean shifted to zero,

Also,P(-2<Z<2)=area of the region between -1 to 1 that is approximately equal to=95%