Question

According to records, the amount of precipitation in a certain city on a November day has a mean of 0.10 inches, with a standard deviation of 0.07 inches. What is the probability that the mean daily precipitation will be 0.11 inches or less for a random sample of November days (taken over many years)?

Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Answer 1

The probability that the mean daily precipitation will be 0.11 inches or less for a random sample of November days

P(X≤ 0.11) = 0.4404

Explanation:

Step(i):-

Given that the mean of the Population = 0.10 inches

Given that the standard deviation of the population = 0.07inches

Let 'X' be a random variable in a normal distribution

`Z = (x-mean)/(S.D) = (0.11-0.10)/(0.07) = 0.1428`

Step(ii):-

The probability that the mean daily precipitation will be 0.11 inches or less for a random sample of November days

P(X≤ 0.11) = P(Z≤0.1428)

= 1-P(Z≥0.1428)

= 1 - ( 0.5 +A(0.1428)

= 0.5 - A(0.1428)

= 0.5 -0.0596

= 0.4404

Final answer:-

The probability that the mean daily precipitation will be 0.11 inches or less for a random sample of November days

P(X≤ 0.11) = 0.4404