Question

The mean height of women in a country (ages 20 - 29) is 64.3 inches. A random sample of 65 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume o = 2.81. The probability that the mean height for the sample is greater than 65 inches is (Round to four decimal places as needed.) Enter your answer in the answer box and then click Check Answer. Clear All All parts showing e​

Answer 1

Answer:  0.4016

Step-by-step explanation:

Let x be a random variable that represents the height of women in a country.

Mean : $\mu=64.3$ inches

Sample size : n= 65

Standard deviation: $\sigma=2.81$

The probability that the mean height for the sample is greater than 65 inches = $P(x>65)=1-P(x<65)$

$=1-P(\dfrac{x-\mu}{\sigma}<\dfrac{65-64.3}{2.81})\\\\= 1-P(z<0.2491)\\\\=1-0.5984\ \ \ \text{[By p-value table]}\\\\=0.4016$

Hence, the probability that the mean height for the sample is greater than 65 inches = 0.4016