# Women have head circumferences that are normally distributed with a m.docx

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Women have head circumferences that are normally distributed with a mean given by mu = 23.32 in, and a standard deviation given by sigma = 0.6 in. Complete parts a through c below. a. if a hat company produces women's hats so that they fit head circumferences between 23.0 in and 24 0in, what is the probability that a randomly selected woman will be able to fit into one of these hats? The probability is (Round to four decimal places as needed.) b. if the company wants to produce hats to fit all women except for those with the smallest 1.5% and the largest 1.5% head circumferences, what head circumferences should be accommodated?
c. If 11 women are randomly selected, what is the probability that their meanhead circumference is between 23.0 in. and 24.0 in.? If this probability is high, does it suggest that an order of 11 hats will very likely fit each of 11 randomly selected women?