Answer :
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.
What is the probability?
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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