Posted: May 26th, 2022

Normal probability distribution | Mathematics homework help

1. The diameters of Red Delicious apples in a certain orchard are normally distributed with a mean of 2.63 inches and a standard deviation of 0.25 inches.

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a. What percentage of the apples in the orchard have diameters less than 1.95 inches?

b. What percentage of the apples in the orchard have diameters larger than 2.90 inches?

c. If a crate of 200 apples is selected from the orchard, approximately how many apples would you expect to have diameters greater than 2.90 inches?

d. What is the probability that a randomly selected apple in this orchard will have a diameter larger than 2.54 inches?

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e. What is the probability that a randomly selected apple in this orchard will have a diameter between 1.95 inches and 2.9 inches? Interpret the meaning of this answer.

2. A radar unit is used to measure the speed of automobile on an expressway during rush-hour traffic. The speeds of individual automobiles are normally distributed with a standard deviation of 4 mph.

a. Find the mean of all speeds if 3% of the automobiles travel faster than 72 mph. Round the mean to the nearest tenth.

b. Using the mean you found in part a, find the probability that a car is traveling between 70 mph and 75 mph. Interpret the meaning of this answer.

c. Using the mean you found in part a, find the 25th percentile for the variable “speed”.

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