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Answer:
Probability that the mean daily precipitation will be 0.09 inches or less for a random sample of 40 November days is 0.103.
Step-by-step explanation:
We are given that 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 0.05 inches.
A random sample of 40 November days is taken(taken over many years).
<u><em>Let </em></u><u><em> = sample mean daily precipitation</em></u>
The z score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean = 0.10 inches
= population standard deviation = 0.05 inches
n = sample of days = 40
Now, the probability that the mean daily precipitation will be 0.09 inches or less is given by = P(
0.09 inches)
P(
0.09 inches) = P(
) = P(Z
-1.265) = 1 - P(Z < 1.265)
= 1 - 0.8971 = <u>0.1029</u>
<em>The above probability is calculated by looking at the value of x = 1.265 from the z table which will lie between x = 1.26 and x = 1.27 which has an area of 0.89617 and 0.89796 respectively.</em>
Hence, the probability that the mean daily precipitation will be 0.09 inches or less for a random sample of 40 November days is 0.103.