Respuesta :
Answer:
The number of women expected to meet the height requirements is 149 women.
Step-by-step explanation:
To solve the question, we note that
The population mean = 63.5 inches
The population standard deviation = 2.2
The range of required height = 58 to 80
We are required to find the proportion of women between the height range
The z value for 58 is given by
[tex]z = \frac{x- \mu}{\sigma}[/tex]
Where:
x = Required statistic
μ = Population mean
σ = Standard deviation
= (58 - 63.5)/2.2 = -2.5 and
From the z-score table, we have P(z= -2.5) = 0.0062
The z value for 80 is given by
= (80 - 63.5)/2.2 = 7.5
From the z-score table, we have P(z= 7.5) ≈ 1
Therefore the proportion of women that satisfy the given range is between the two given probabilities, that is P(z= 7.5) - P(z= -2.5) or
1 - 0.0062 ≈ 0.994
Therefore the the number of women expected to meet the criteria is
150 × 0.994 = 149.07 ≈ 149 women out of 150 women meet the criteria.
