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 ...

... The normal distribution maximizes the information randomness among all distributions with known mean and variance, which makes it the natural choice of ...

...normal For fairly symmetric distributions, n > 15 For normal population distributions, the sampling distribution of the mean is always normally distributed. ...

... 3) The probability that a standard normal random variable, Z is ... of the following sentences best describes the distributions A)The distribution is perfectly ...

... What is the difference between discrete and continuous probability distributions? How would you apply the normal distribution to facilitate business decision ...

Problems with Normal Distribution. ... a. If sales follow a normal distribution with µ = 70,000 and = 5,000 per day, how many loaves should Amazing bake daily? ...