Question

The height for the population of women in their 20s is normally distributed with mean 64.1 inches and standard deviation 2.75 inches.  When samples of size 40 are taken from this population, the sampling distribution has mean 64.1 inches and standard deviation 0.4348.  What is the z-score if we want to find the probability that a single woman is less than 60 inches tall?

Answer 1

Answer: To find the z-score for the probability that a single woman is less than 60 inches tall, we can use the formula for calculating the z-score:

z = (x - μ) / σ

where:

x = the individual value (in this case, 60 inches)

μ = the mean of the population (64.1 inches)

σ = the standard deviation of the population (2.75 inches)

Now, let's plug in the values and calculate the z-score:

z = (60 - 64.1) / 2.75

z = -4.1 / 2.75

z ≈ -1.4909 (rounded to four decimal places)

The z-score for the probability that a single woman is less than 60 inches tall is approximately -1.4909.