Respuesta :
Answer: The probability that the height of a selected woman's height is between 65.5 and 68.0 is 0.21
Step-by-step explanation:
Assume that the heights of women are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = heights women.
µ = mean height
σ = standard deviation
From the information given,
µ = 63.6 inches
σ = 2.5 inches
The probability that the height of a selected woman's height is between 65.5 and 68.0 inches is expressed as
P(65.5 ≤ x ≤ 68)
For x = 65.5,
z = (65.5 - 63.6)/2.5 = 0.76
Looking at the normal distribution table, the probability corresponding to the z score is 0.7764
For x = 68,
z = (68 - 63.6)/2 = 2.2
Looking at the normal distribution table, the probability corresponding to the z score is 0.986
Therefore,
P(65.5 ≤ x ≤ 68) = 0.986 - 0.7764 = 0.21
