consider the probability that less than 16 out of 151 people have been in a car...

consider the probability that less than 16 out of 151 people have been in a car accident. assume the probability that a given person has been in a car accident is 12%. Approximate the probability using the normal distribution. Round to four decimal places.

Expert Solution

Probability that a given person has been in a car accident, p = 12% = 0.12

The given sample size n = 151

Let X be the number of people have been in a car accident out of 151 people. Then X ~ Binomial(n = 151, p = 0.12)

Mean = np = 151 * 0.12 = 18.12

Standard deviation = = 3.993194

Assuming normal approximation to binomial distribution,

P(X < 16) = P(X < 15.5) (Using continuity correction)

= P[Z < (15.5 - 18.12) / 3.993194]

= P[Z < -0.6561]

= 0.2559

orchestra answered 2 years ago

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