Question

A normal population has a mean of 57 and a standard deviation of 19. You select a random sample of 19. Use Appendix B.1 for the z-values. Compute the probability that the sample mean is: (Round the final answers to 4 decimal places.)

a. Greater than 60.

Probability

b. Less than 53.

Probability

c. Between 53 and 60.

Probability

Answer 1

Solution :

= / n = 19 / 19 = 4.3589

(a)

P( > 60) = 1 - P( < 60)

= 1 - P[( - ) / < (60 - 57) / 4.3589]

= 1 - P(z < 0.69)

= 0.2451

Probability = 0.2451

(b)

P( < 53) = P(( - ) / < (53 - 57) / 4.3589)

= P(z < -0.92)

= 0.1788

Probability = 0.1788

(c)

P(53 < < 60)

= ( < 60) - P( < 53)

= 0.7549 - 0.1788

= 0.5761

Probability = 0.5761