1)Use the normal distribution of fish lengths for which the mean is 9 inches and
ID: 3333805 • Letter: 1
Question
1)Use the normal distribution of fish lengths for which the mean is 9 inches and the standard deviation is 2 inches. Assume the variable x is normally distributed. left parenthesis a right parenthesis
(a) What percent of the fish are longer than 12 inches?
(b) If 300 fish are randomly selected, about how many would you expect to be shorter than 6 inches?
(a) Approximately % of fish are longer than 12 inches.
(Round to two decimal places as needed.)
(b) You would expect approximately fish to be shorter than 6 inches. (Round to the nearest fish.)
2)The time spent (in days) waiting for a kidney transplant for people ages 35-49 can be approximiated by the normal distribution, as shown in the figure to the right.
(a) What waiting time represents the 98th percentile?
(b) What waiting time represents the first quartile?
u=1679
=212.9
1579, 1679, 1779 days
(a) The waiting time that represents the 98th percentile is
days.
(Round to the nearest integer as needed.)
(b) The waiting time that represents the first quartile is
days.
(Round to the nearest integer as needed.)
3)Find the probability and interpret the results. If convenient, use technology to find the probability.
The population mean annual salary for environmental compliance specialists is about 61,000. A random sample of 43 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $59,000? Assume =$5,900.
The probability that the mean salary of the sample is less than $59,000 is
(Round to four decimal places as needed.)
Interpret the results. Choose the correct answer below.
A.Only 13.1% of samples of 43 specialists will have a mean salary less than 59,000. This is an unusual event.
B.About 13.1% of samples of 43 specialists will have a mean salary less than 59,000. This is not an unusual event.
C.About 1.31% of samples of 43 specialists will have a mean salary less than 59,000. This is not an unusual event.
D.Only 1.31% of samples of 43 specialists will have a mean salary less than $59,000. This is an unusual event.
Explanation / Answer
mean is 9 inches and standard deviation is 2 inches. z is given as (x-mean)/s
(a) P(x>12)= P(z>(12-9)/2)=P(z>1.5) or 1-P(z<1.5), from normal table we get 1-0.9332=0.0668
(b) If 300 fish are randomly selected, about how many would you expect to be shorter than 6 inches?
Standard error , SE is given as s/sqrt(N) =2/sqrt(300)=0.1155
thus P(x<6)=P(z<(6-9)/0.1155)=P(z<-25.97), thus it is 0
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