The distribution of the number of dill pickle spears in a gallon container is ap

Question

The distribution of the number of dill pickle spears in a gallon container is approximately Normal with mean 110 and standard deviation 10.

Approximately what percent of the containers had fewer than 105 spears?

The median number of pickle spears for this sort of container:

a) is less than 110 spears.

b) is equal to 110 spears.

c) is greater than 110 spears.

d) could be anywhere between 100 points and 120 spears.

e) is unknown—it could be either less than 110 points or greater than 110 points.

Approximately what percent of the containers had fewer than 105 spears?

How many dill pickle spears does a container hold if its standardized score is 0.4? A container with a standardized score of 0.4 is at the 65.54th percentile. What percent of the containers held more pickle spears than this container?

The median number of pickle spears for this sort of container:

a) is less than 110 spears.

b) is equal to 110 spears.

c) is greater than 110 spears.

d) could be anywhere between 100 points and 120 spears.

e) is unknown—it could be either less than 110 points or greater than 110 points.

Explanation / Answer

a) P(X < 105)

= P(z < (105 - 110)/10)

= P(z < -0.5)

= 0.3085

b) Number of Dill pickle spears for such a container = 110 + 0.4(10) = 114

c) Since the container with a standardized score of 0.4 is at the 65.54th percentile,

Percent of containers held more than this container = 100 - 65.54 = 34.46%

d) Since the distribution is only approximately normal, median is unknown and could be either less than 110 points or greater than 110 points.

Option e) is correct.

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