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# Finding probability for standard normal variable

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28) police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the response time has a normal distribution with a mean of 8.4 minutes and a standard deviation of 1.7 minutes. for a randomly received emergency call, what is the probability that the response time will be
a) between 5-10 minutes (answer key says: .8036) but i need to show work
b) less than 5 minutes (answer key: .0228) need to show work
c) more than 10 minutes (answer key .1736) need to show work

32)
estimating the standard deviation: refrigerator replacement:
the average life of a refrigerator before replacement is u=14 years with a (95%of data) range from 9-19 years. let x= age at which refrigerator is replaced. Assume that x has a distribution that is approximately normal.
a) find a good approximation for the standard deviation of x values.
(answer key: 2.5 years) but need to show work
b) what is the probability that someone will keep the refrigerator fewer than 11 years before replacement? (answer .1151) need to show work
c) what is the probability someone will keep more than 18 years? (answer .0548) need to show work
d) inverse normal distribution: Assume that the average life of a fridge is 14 years with a standard deviation given in part a) before it breaks. suppose that a company guarantees frigerators and will replace it under guarantee with a new one. However the company does not want to replace more than 5% of the fridges under guarantee. how long should the guarantee be made? (answer 9.9 years) need to show work

36)Attendance at a large show in Denver averages 8,000 people per day with a standard deviation of 500. assume the daily attendance figures follow a normal distribution

a) what is the probability the daily attendance will be fewer than 7200? (answer .0548) need to show work
b) more than 8900 people? (answer .0359) show work
c) what is the probability daily attendance will be between 7200 and 8900'? (answer: .9093 need to show work)

6.4
8
Ocean fishing for "billfish" is very popular in Mexico. it is stated that in this area 44% of strikes (while fishing)result in a catch. Suppose on a given day a fleet of fishing boats got a total of 24 strikes. what is the probability the number of fish caught was
a)12 or fewer (answer .7881) need to show work
b) 5 or more (answer .9936) need to show work
c) between 5-12 (answer .7817) need to show work

10. What are the chances a person who is murdered actually knew the killer? 64% of people who are killed actually know the person who did it. suppose a detective file in new orleans has 63 current unsolved murders. what is the probability that:
a) at least 35 victims knew their murderer (answer: .9370) need to show work
b) at most 48 victims knew killer (answer .9842) need to show work
c) 30 victims did not know their killer (.9633)
d)more than 20 victims did not know their killer (.7157)

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#### Solution Preview

28) police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the response time has a normal distribution with a mean of 8.4 minutes and a standard deviation of 1.7 minutes. for a randomly received emergency call, what is the probability that the response time will be
a) between 5-10 minutes (answer key says: .8036) but i need to show work
Now z=(x-u)/sd=(x-8.4)/1.7.
So P(5<X<10)=P((5-8.4)/1.7<Z<(10-8.4)/1.7)=P(-2<Z<0.94)=0.8036 from standard normal table.
b) less than 5 minutes (answer key: .0228) need to show work
P(X<5)=P(Z<(5-8.4)/1.7)=P(Z<-2)=0.0228 from standard normal table.
c) more than 10 minutes (answer key .1736) need to show work
P(X>10)=P(Z>(10-8.4)/1.7)=P(Z>0.94)=0.1736 from standard normal table.

32)
estimating the standard deviation: refrigerator replacement:
the average life of a refrigerator before replacement is u=14 years with a (95%of data) range from 9-19 years. let x= age at which refrigerator is replaced. Assume that x has a distribution that is ...

#### Solution Summary

The solution gives detailed steps on calculating the probability under the curve of the standard normal distribution. All formula and calculations are shown and explained.

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