07 Jan Select the correct choice
Homework 3
1. Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
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2. Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
3. Find the area of the shaded region. The graph to the right depicts IQ scores of? adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
4. Find the area of the shaded region. The graph to the right depicts IQ scores of? adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
5. Find the indicated IQ score. The graph to the right depicts IQ scores of? adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
6. A survey found that? women’s heights are normally distributed with mean 62.6 in. and standard deviation 2.3 in. The survey also found that? men’s heights are normally distributed with a mean 68.3 in. and standard deviation 2.8. Complete parts a through c below.
a. Most of the live characters at an amusement park have height requirements with a minimum of 4 ft 9 in. and a maximum of 6 ft 3 in. Find the percentage of women meeting the height requirement.
The percentage of women who meet the height requirement is _____?(Round to two decimal places as? needed.)
b. Find the percentage of men meeting the height requirement.
The percentage of men who meet the height requirement is ______?(Round to two decimal places as? needed.)
c. If the height requirements are changed to exclude only the tallest? 5% of men and the shortest? 5% of? women, what are the new height? requirements?
The new height requirements are at least _____and at most ______?(Round to one decimal place as? needed.)
7. Which of the following is NOT a property of the sampling distribution of the sample? mean?
Choose the correct answer below.
A.
The distribution of the sample mean tends to be skewed to the right or left.
B.
The mean of the sample means is the population mean.
C.
The sample means target the value of the population mean.
D.
The expected value of the sample mean is equal to the population mean.
8. Assume that? women’s heights are normally distributed with a mean given by mu equals 64.1 in?, and a standard deviation given by sigma equals 2.6 in.
?(a) If 1 woman is randomly? selected, find the probability that her height is less than 65 in.
?(b) If 31 women are randomly? selected, find the probability that they have a mean height less than 65 in.
?(?a) The probability is approximately ?(Round to four decimal places as? needed.)
?(b) The probability is approximately ?(Round to four decimal places as? needed.
9. An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb and 211 lb. The new population of pilots has normally distributed weights with a mean of 158 lb and a standard deviation of 31.2 lb.
a. If a pilot is randomly? selected, find the probability that his weight is between 150 lb and 211 lb.
The probability is approximately _________?(Round to four decimal places as? needed.)
b. If 33 different pilots are randomly? selected, find the probability that their mean weight is between 150 lb and 211 lb.
The probability is approximately _______?(Round to four decimal places as? needed.)
c. When redesigning the ejection? seat, which probability is more? relevant?
A.
Part? (b) because the seat performance for a single pilot is more important.
B.
Part? (a) because the seat performance for a sample of pilots is more important.
C.
Part? (b) because the seat performance for a sample of pilots is more important.
D.
Part? (a) because the seat performance for a single pilot is more important.
10. If np greater than or equals 5 and nq greater than or equals 5?, estimate Upper P left parenthesis fewer than 6 right parenthesis with nequals13 and pequals0.6 by using the normal distribution as an approximation to the binomial? distribution; if npless than5 or nqless than?5, then state that the normal approximation is not suitable.
Select the correct choice below? and, if? necessary, fill in the answer box to complete your choice.
A.
Upper P left parenthesis fewer than 6 right parenthesis = ___?(Round to four decimal places as? needed.)
.B.
The normal approximation is not suitable
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