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2 years ago

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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.

1 answer:

Andru [333]2 years ago

8 0

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

Step-by-step explanation:

<u><em>Step(i):-</em></u>

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

$Z = \frac{x-mean}{S.D} = \frac{0.11-0.10}{0.07} = 0.1428$

<u><em>Step(ii):-</em></u>

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

<u><em>Final answer:-</em></u>

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

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