Let X denote the number of neutrophils (a special type of white blood cell) in 50randomly sampled white blood cells. If, overall 40% of white blood cells are neutrophils, describethe distribution of X. Compute approximately the probability thatX <15? EXPLAIN THETOOL(S) you are using to compute this probability. Note that you should not be computing theexact probability, as you are not allowed to use a scientific computer that would be necessary tocompute this number.

The probability of X < 15 is 0.054.

Step-by-step explanation:

The random variable X is defined as the number of neutrophils.

The number of white blood cells sampled is, n = 50.

The proportion of neutrophils is, p = 0.40.

A randomly sampled white blood cells is a neutrophil or not is independent of all the other white blood cells.

The random variable X thus follows a Binomial distribution with parameters n = 50 and p = 0.40.

The probability mass function of the Binomial distribution is:

Compute the probability of X < 15 as follows:

Thus, the probability of X < 15 is 0.054.

step-by-step explanation:

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