NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 15 children and let X be the number in the sample who have a food allergy. Then X Bins, 0.05). (Round your probabilities to three decimal places) (a) Determine both PX S 3) and Px 3) (b) Determine P(X 2 4) (c) Determine Pi s x 3). (d) what are E(a) and ax? (Round your aswers to twe decimal places) (e) [email protected] of 90 children, what is the probability that none has food allergy?

Part a: The value of P(X≤3) is 0.995 while that of P(X<3) is 0.964

Part b: The value of P(X≥4) is 0.005

Part c: The value of P(1≤X≤3) is 0.531

Part d: The expected value of mean is 0.75 while that of standard deviation is 0.844.

Part e: The probability that none has allergy in 90 children in 0.010.

Step-by-step explanation:

Part a

For the value is given as

Here p=0.05, n=15 so the values are given as

So

So the value of P(X≤3) is 0.995

For the value is given as

Here p=0.05, n=15 so the values are given as

So

So the value of P(X<3) is 0.964

Part b

For the value is given as

Here p=0.05, n=15 so the values are given as

So

So the value of P(X≥4) is 0.005

Part c

For the value is given as

Here p=0.05, n=15 so the values are given as

So

So the value of P(1≤X≤3) is 0.531

Part d

The expected value of mean is given as

Here n =15, p =0.05

The expected value of mean is 0.75

While the expected value of the standard deviation is given as

Here n =15, p =0.05

So the expected value of standard deviation is 0.844

Part e

For the value is given as

Here p=0.05, n=90 so the values are given as

So the probability that none has allergy in 90 children in 0.010.

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step-by-step explanation: