The average height of a woman aged 20-29 is 64 inches with a standard deviation of 2.75 inches. What is the probability of selecting 25 women with average height more than 65 inches?

Answer:The probability of selecting 25 women with average height more than 65 inches is  0.036Step-by-step explanation:To calculate the probability of selecting 25 women with average height more than 65 inches, we need to calculate the z-statistic of the sample with average height 65 inches. z-score can be calculated as follows:z(65) = [tex]\frac{X-M}{\frac{s}{\sqrt{N} } }[/tex] where X = 65 inchesM is the average height of women aged 20-29 (64 inches)s is the standard deviation (2.75 inches)N is the sample size (25)Then z(65) = [tex]\frac{65-64}{\frac{2.75}{\sqrt{25} } }[/tex] ≈ 1.818The probability of a statistic being bigger then this statistic is 0.036