Assume that women's weights are normally distributed with a mean given by [tex]\mu = 143 \text{ lb}[/tex] and a standard deviation given by [tex]\sigma = 29 \text{ lb}[/tex].

(b) If 4 women are randomly selected, find the probability that they have a mean weight below 108 lb.

(c) If 58 women are randomly selected, find the probability that they have a mean weight below 108 lb.

Question

High School

Answer :

mickymike92 mickymike92 · Answer 1 · 2024-06-21T07:38:20-04:00

The probability that 4 women have a mean weight below 108 lb is approximately 0.008.

The probability that 58 women have a mean weight below 108 lb is zero.

The probability is determined using the central limit theorem.

(b) If 4 women are randomly selected, the sample mean weight (x) will also be normally distributed:

mean = 143 lb

standard deviation = 29/√(4)

standard deviation = 14.5 lb.

We can use the z-score formula to find the probability that the sample mean weight is below 108 lb:

z = (108 - 143) / 14.5

z = -2.41

Using a standard normal distribution table or calculator, the probability of z being less than -2.41 is approximately 0.008.

(c) If 58 women are randomly selected, the sample mean weight (x) will also be normally distributed:

mean = 143 lb

standard deviation = 29/√(58)

standard deviation = 3.81 lb

We can use the z-score formula to find the probability that the sample mean weight is below 108 lb:

z = (108 - 143) / 3.81 ≈ -9.21

Using a standard normal distribution table or calculator, the probability of z being less than -9.21 is extremely small, practically zero.

Learn more about probability and normal distribution at: https://brainly.com/question/4079902

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