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The probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is, 0.9192
What is standard deviation?
The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.
Given: The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 90 inches, and a standard deviation of 14 inches.
z score is given by,
z = (x - μ)/(σ/√n) = (92.8 - 90)/(14/√49) = 2.8/2 = 1.4
The required probability is,
p(z < 1.4) = 0.9192, by standard normal table.
Hence, the probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is, 0.9192.
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