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normal distribution

The average monthly gasoline purchase for a family with 2 cars is 90 gallons. This statistic has a normal distribution with a standard deviation of 10 gallons. A family is chosen at random.
(a) Find the probability that the family's monthly gaoline purchases will be between 88 and 98 gallons.
(b) Find the probability that the family's monthly gasoline purchases will be less than 100 gallons.
(c) Find the probability that the family's monthly gasoline purchases will be more than 78 gallons.

Solution Preview

(a) Find the probability that the family's monthly gasoline purchases will be between 88 and 98 gallons.

P(88 < x < 98) = P(88 < x < 90) + P(90 < x < 98) where mean = 90.

Find P(88 < x < 90):
(1) Find z-score of 88:
z = (x - mean)/stdDev = (88 - 90)/10 = -0.2
(2) From the z-distribution table, the corresponding probability for z = 0.2 is 0.5793, this is the probability for when the value x is on the right of the mean.
Since our z value is on the left of ...

Solution Summary

Find the probability in these cases.

$2.19