Question

g The exchange rate from US Dollars (USD) to Indian Rupee (INR) is normally distributed with an average of 67.43 and a standard deviation of 1.2. What is the exchange rate for the 20th percentile? Enter your answer to 4 decimal places.

Answer 1

The exchange rate for the 20th percentile is 66.422

Explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

`\mu = 67.43 \sigma = 1.2`

What is the exchange rate for the 20th percentile?

This is X when Z has a pvalue of 0.2. So it is X when Z = -0.84.

`Z = (X - \mu)/(\sigma)`

`-0.84 = (X - 67.43)/(1.2)`

`X - 67.43 = -0.84*1.2`

`X = 66.422`

The exchange rate for the 20th percentile is 66.422