Respuesta :
Answer:
Step-by-step explanation:
Since 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 of women.
µ = mean height
σ = standard deviation
From the information given,
µ = 65 inches
σ = 2.5 inches
The probability that a woman is taller than 70 inches is expressed as
P(x > 70) = 1 - P(x ≤ 70)
For x = 70
z = (70 - 65)/2.5 = 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.977
Therefore,
P(x > 70) = 1 - 0.977 = 0.023
The percent of women that are taller than a man of average height is 0.023 × 100 = 2.3℅
The percent of women that are taller than a man of average height is 2.3℅
Calculation of the percentage:
Since The heights of women are normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches. The heights of men are also normal with a mean of 70 inches.
So,
The probability that a woman is taller than 70 inches should be
P(x > 70) = 1 - P(x ≤ 70)
Now
For x = 70
[tex]z = (70 - 65)\div 2.5 =[/tex] 2
Now we look at the normal distribution table, the probability corresponding to the z score is 0.977
So,
P(x > 70) = 1 - 0.977
= 0.023
Hence, we can conclude that The percent of women that are taller than a man of average height is 2.3℅
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