Question

A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 62 months and a standard deviation of 5 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 67 and 72 months? ans = __ %

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P₇₆, the 76-percentile. This is the temperature reading separating the bottom 76% from the top 24% (round to three deimcal places).

P₇₆ = ____°C

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested.

If 2% of the thermometers are rejected because they have readings that are too high and another 2% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others.

interval of acceptable thermometer readings = _____°C

Answer 1

A) According to emperical rule 68% of the data falls within one standard deviation from the mean and 95% of the data falls within two standard deviation from the mean.

67 is one standard deviation above the mean. So 34% of the data falls within mean 62 and 67

Similarly 72 is two standard deviation from the mean. So 47.5% of the data falls within mean 62 and 72.

S0 47.5% - 34% = 13.5% of cars that remain between 67 and 72 months.

B) P(X < x) = 0.76

or, P(Z < z) = 0.76

or, z = 0.71

or, (x - 0)/1 = 0.71

or, x = 0.71

P76 = 0.71

c) P(X < x) = 0.02

or, P(Z < z) = 0.02

or, z = -2.05

or, (x - 0)/1 = -2.05

or, x = -2.05

P(X > x) = 0.02

or, P(Z > z) = 0.02

or, P(Z < z) = 0.98

or, z = 2.05

or, (x - 0)/1 = 2.05

or, x = 2.05

Interval of acceptable thermometer readings = -2.05 to 2.05