Women have head circumferences that are normally distributed with a mean given b
ID: 3050086 • Letter: W
Question
Women have head circumferences that are normally distributed with a mean given by mu equals 22.93 in ., and a standard deviation given by sigma equals 1.1 in. Complete parts a through c below. a. If a hat company produces women's hats so that they fit head circumferences between 22.7 in. and 23.7 in., what is the probability that a randomly selected woman will be able to fit into one of these hats? b. If the company wants to produce hats to fit all women except for those with the smallest 2.5 % and the largest 2.5 % head circumferences, what head circumferences should be accommodated? c. If 19 women are randomly selected, what is the probability that their mean head circumference is between 22.7 in. and 23.7 in.? If this probability is high, does it suggest that an order of 19 hats will very likely fit each of 19 randomly selected women? Why or why not? (Assume that the hat company produces women's hats so that they fit head circumferences between 22.7 in. and 23.7 in.)
Explanation / Answer
a)
probability that a randomly selected woman will be able to fit into one of these hats :
b)
for 2.5% tails ends ; z score =-/+1.96
therefore corresponding hat circumference =mean -/+ z*std deviation =20.77 ; 25.09
c)
d)
No; as individal has to waer the hat ; not the group and probability for an individual is less,
for normal distribution z score =(X-)/ here mean= = 22.930 std deviation == 1.1Related Questions
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