Question

In: Statistics and Probability

In a popular headache medicine, the amount of active ingredient per pill follows a normal distribution...

In a popular headache medicine, the amount of active ingredient per pill follows a normal distribution with a mean of 505 mg and a standard deviation of 2.1 mg. X represents the amount of the active ingredient in each pill. Enter the mean and standard deviation into the Normal CDF Calculator to find the probabilities.

a) What is the probability that a single pill of the medicine contains less than 500 mg of active ingredient?
P(X < 500) =

b) What is the probability that a single pill of the medicine contains more than 500 mg of active ingredient?
P(X > 500) =

c) What is the probability that a single pill of the medicine contains more than 509 mg of active ingredient?
P(X > 509) =

d) What is the probability that a single pill of the medicine contains between than 500 and 505 mg of active ingredient?
P(500 < X < 505) =

Solutions

Expert Solution

Refer Standard normal table/Z-table to find the probability OR use excel formula "=NORM.S.DIST(-2.38, TRUE)" to find the probability.

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Note: P(Z>a)=1-P(Z<a)

Refer Standard normal table/Z-table to find the probability OR use excel formula "=NORM.S.DIST(-2.38, TRUE)" to find the probability.

-------------------------------------------------------------------------------------------------

Note: P(Z>a)=1-P(Z<a)

Refer Standard normal table/Z-table to find the probability OR use excel formula "=NORM.S.DIST(1.90, TRUE)" to find the probability.

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Note: P(a<Z<b)=P(Z<b)-P(Z<a)

Refer Standard normal table/Z-table to find the probability or use excel formula "=NORM.S.DIST(0.00, TRUE)" & "=NORM.S.DIST(-2.38, TRUE)" to find the probability.

orchestra answered 2 years ago
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