SOLUTION: a normal pop has a mean of 75 and a stan dev of 5. you select a sample size of 40. compute the probability the sample mean is: less than 74 btwn 74 and 76 btwn 76 and 77 grea

Algebra ->  Probability-and-statistics -> SOLUTION: a normal pop has a mean of 75 and a stan dev of 5. you select a sample size of 40. compute the probability the sample mean is: less than 74 btwn 74 and 76 btwn 76 and 77 grea      Log On


   

Question 889578: a normal pop has a mean of 75 and a stan dev of 5. you select a sample size of 40. compute the probability the sample mean is:
less than 74
btwn 74 and 76
btwn 76 and 77
greater than 77
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
With a sample size > 30, we can use the population's standard dev of 5. The mean of the population applies to the sample no matter its size.
z-value = (X - mean) / std dev
A. z-value = (74 - 75) / 5 = -0.20
consult table of z-values for associated probability
P(X < 74) = 0.4207
B. z-value = (76 - 75) / 5 = 0.20
P(74 < X < 76) is P(X < 76) - P(X < 74) = 0.5793 - 0.4207 = 0.1586
C. z-value = (77 - 75) / 5 = 0.40
P(76 < X < 77) is P(X < 77) - P(X < 76) = 0.6554 - 0.5793 = 0.0761
D. P(X > 77) is 1 - P(X < 77) = 1 - 0.6554 = 0.3446