Question

A study of the adequacy of New York City’s snow-fighting capability estimated that the number of snowstorms in a season was approximately (remember the continuity approximation) normally distributed with a mean of 6.5 and a standard deviation of 2.25. How often does New York City have more than 10 snowstorms in a season? Assuming independence, what is the probability that New York City will have more than 10 snowstorms in at least two of the next three seasons?

Answer 1

0.05991, 0.003589

Explanation:

Given that a study of the adequacy of New York City’s snow-fighting capability estimated that the number of snowstorms in a season was approximately (remember the continuity approximation) normally distributed with a mean of 6.5 and a standard deviation of 2.25.

X- number of snowstorms is N(6.5,2.25)

`P(X>10)\\= P(Z>1.56)\\\\=0.05991`

Assuming independence we can say Y the no of snowstorms >=2 is

Binomial with n =3, and p = 0.05991

the probability that New York City will have more than 10 snowstorms in at least two of the next three seasons

=
`0.05991^2\\=0.003589`