# What is the probability that 5 of the next 11 capsules contain less than 4.95 mg of viatamin E?A machine producing vitamin E operates so that the actual amount of vitamin E in each capsule is...

What is the probability that 5 of the next 11 capsules contain less than 4.95 mg of viatamin E?

A machine producing vitamin E operates so that the actual amount of vitamin E in each capsule is normally distributed with mean 5mg and standard deviation 0.05 mg.

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### 1 Answer

The machine producing vitamin E operates so that the actual amount of vitamin E in each capsule is normally distributed with a mean value in each capsule of 5mg and standard deviation 0.05 mg.

The probability that any 5 of 11 capsules chosen contains less than 4.95 mg of vitamin E has to be determined.

First calculate the probability that any random capsule has an amount of vitamin E less that 4.95 mg.

The z-score for 4.95 is (4.95 - 5)/0.05 = -1

The corresponding probability is 0.1587.

The number of ways of choosing 5 tablets out of 11 is C(11, 5) = 462

As each has a probability of 0.1587 of having less than 4.95 mg of vitamin E, the required probability is 462*0.1587 = 73.31%

**There is a 73.31% probability that any 5 out of 11 capsules contain less than 4.95 mg of vitamin E.**

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