Answer:
a) 0.586
b) 0.846
c) We are more likely to select a sample of 22 woman with a mean height of 64.9 inches.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 64.4 inches
Standard Deviation, σ =2.3 inches
We are given that the distribution of height of woman is a bell shaped distribution that is a normal distribution.
Formula:
a) P(selecting 1 woman with a height less than 64.9 inches)
P(x < 64.9)
Calculation the value from standard normal z table, we have,
b) P(selecting 22 woman with a height less than 64.9 inches)
Standard error due to sampling =
P(x < 64.9)
Calculation the value from standard normal z table, we have,
c) Since,
P(selecting 22 woman with a height less than 64.9 inches) > P(selecting 1 woman with a height less than 64.9 inches)
We are more likely to select a sample of 22 woman with a mean height of 64.9 inches.