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 $35$ and $45$ minutes to complete the questionnaire?

• A. About $68\%$
• B. About $72\%$
• C. About $76\%$
• D. About $84\%$

Answer 1

Answer: (A)

About $68\%$

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 35 to 45 min i.e, P(35<x<45)

For standard normal distribution curve

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

(35-40)/5<(x-$\mu$)/$\sigma$<(45-40)/5

-1<Z<1

For standard normal distribution mean shifted to zero,

Also,P(-1<Z<1)=area of the region between -1 to 1 that is approximately equal to=68%