The average (mean) amount of time that a manager at the mount

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1. MBB Problem 7.2 (modified)

The average (mean) amount of time that a manager at the Mount Pleasant Department of Human Services spends in the annual performance review with an employee is 27.2 minutes, with a standard deviation of 4.9 minutes (normal distribution).

(a) What percentage of the annual performance reviews in the department take between 22.3 and 32.1 minutes?

(b) Between 17.4 and 37 minutes?

(c) Between 12.5 and 41.9 minutes?

2. MBB Problem 7.6 (modified)

Refer to Problem 7.5 (which we covered in lecture). 

MBB Problem 7.5
> • Parnelli Jones, a vehicle manager for the northeast region of the forestry service, is
> charged with purchasing automobiles for service use. Because forestry service
> employees often have to drive long distances in isolated regions, Parnelli is very
> concerned about gasoline mileage for the vehicle fleet. One automobile
> manufacturer has told him that the particular model of vehicle that interests him
> has averaged 27.3 miles per gallon in road tests with a standard deviation of 3.1
> (normal distribution). Parnelli would like to be able to tell his superiors at the
> forestry service that the cars will get at least 25 miles to the gallon. According to
> the road test data, what percentage of the cars can be expected to meet this
> criterion?
>
> • Parnelli also thinks that his superiors might settle for cars that got 24 miles to the
> gallon or better. What percentage of the cars can be expected to meet this
> criterion?
>

(a) During the negotiations with the automobile manufacturer, Parnelli gets a sinking feeling that some of the cars he is thinking of purchasing for the forestry service might average less than 20 

miles to the gallon of gasoline. According to the road test data, what percentage of the cars can be expected to fall below this mileage level? Should Parnelli be very worried?

(b) Parnelli wants to be able to tell his superiors that at least 90% of cars purchased from this manufacturer will get a certain number of miles per gallon. Help him find the miles per gallon number that he can expect 90% of these cars to exceed.