Question

The summer monsoon rains bring 80 % of India's rainfall and are essential for the country's agriculture. Records going back more than a century show that the amount of monsoon rainfall varies from year to year according to a distribution that is approximately Normal with mean 852 millimeters (mm) and standard deviation 82 mm. Use the 68 ‑ 95 ‑ 99.7 rule to answer the questions. (a) Between what values do the monsoon rains fall in the middle 95 % of all years?

Answer 1

Answer:

95% of monsoon rainfall lies between 688 mm and 1016 mm.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 852 mm

Standard Deviation, σ = 82 mm

We are given that the distribution of monsoon rainfall is a bell shaped distribution that is a normal distribution.

68 ‑ 95 ‑ 99.7 rule

• Also known as Empirical rule.
• It states that all data lies within the three standard deviation of the mean for a normal distribution.
• About 68% of data lies within one standard deviation of mean
• About 95% of data lies within two standard deviation of mean.
• About 99.7% of data lies within three standard deviation of mean.

We have to find the monsoon rains fall in the middle 95 % of all years.

By the rule 95% of data lies within two standard deviation of mean.Thus,

$\mu + 2\sigma = 852 + 2(82) = 1016\\\mu - 2\sigma = 852 - 2(82) = 688$

Thus, 95% of monsoon rainfall lies between 688 mm and 1016 mm.