A leading magazine (like Barron\'s) reported at one time that the average number

Question

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 33 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 33 weeks and that the population standard deviation is 9.4 weeks. Suppose you would like to select a random sample of 81 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 33.6 and 34.3. P(33.6 < X < 34.3) = Find the probability that a sample of size n = 81 n=81 is randomly selected with a mean between 33.6 and 34.3. P(33.6 < M < 34.3) =

Explanation / Answer

Mean is 33 and s is 9.4

a) P(33.6 < X < 34.3) =P((33.6-33)/9.4<z<(34.3-33)/9.4)=P(0.06<z<0.14)=P(z<0.14)-P(z<0.06). from normal distribution table we get 0.5557-0.5239=0.0318

b) Standard error is 9.4/sqrt(81)=9.4/9=1.044

thus P(33.6 < X < 34.3) =P((33.6-33)/1.044<z<(34.3-33)/1.044)=P(0.57<z<1.25) or P(z<1.25)-P(z<0.57)

from normal table we get 0.8944-0.7157=0.1787

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.