Question

Consider the probability that less than 17 out of 160 people will get the flu this winter. Assume the probability that a given person will get the flu this winter is 14%. Approximate the probability using the normal distribution. Round your answer to four decimal places.

Answer 1

Answer:

0.1094

Step-by-step explanation:

Given that we are considering less than 17 out of n= 160, so the required probability is:

P(X< 17)

The probability, p, that a person get the flu is 14%

p = 0.14, q =1 - 0.14 = 0.86

We deduce the mean number of people and the standard deviation using

U = np = 160 × 0.14 = 22.4

Sd =√npq =√ 160 × 0.14 × 0.86

= 4.389

Therefore Probability for less than 17 is given by:

P(X< 17) = P(Z< X-U/sd)

P(X< 17) = P(Z<17-22.3/4.389)

= P(Z< -1.23)

= 0.10935

0.1094

Since we are approximating the distribution to normal distribution