please check and let me know I\'m unsure about the answers thank you Standand fl

Question

please check and let me know I'm unsure about the answers thank you

Standand flornal Disibha 2. A survey was conducted to measure the heights x, in inches, of U.S. women. In the survey the espondents were grouped by age. In the 20-29 years age group, heights are assumed normally distributed and have a mean ?-65.8 inches and a standard deviation o-32 inches. A study participant was randomly selected. Use the z-score formula shown below to find appropriate areas for probabilities in the 20-29 years age group of the following: a) Find the probability that her height is less than 63 inches. P(x

Explanation / Answer

Solution :

Given that mean ? = 65.8 , standard deviation ? = 3.2

a) P(x < 63) = P((x - ?)/? < (63 - 65.8)/3.2)

= P(Z < -0.875)

= 0.1894 or 18.94%

b) P(65 < x < 69) = P((65 - 65.8)/3.2 < Z < (69 - 65.8)/3.2)

= P(-0.25 < Z < 1)

= 0.44 or 44%

c) P(x > 70) = P((x - ?)/? > (70 - 65.8)/3.2)

= P(Z > 1.3125)

= 0.0951 or 9.51%

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