Question

The incomes of a group of 10,000 persons were found to be normally distributed with a mean equal to Rs. 750 and standard deviation equal to Rs. 50. What was the lowest income among the richest 250?

a. Rs. 900
b. Rs. 700
c. Rs. 850
d. Rs. 800

Answer 1

The lowest income among the richest 250 individuals in a group of 10,000 people with a normal distribution can be found using z-scores. The lowest income is Rs. 675.75.

Step-by-step explanation:

The question asks for the lowest income among the richest 250 individuals in a group of 10,000 people whose incomes follow a normal distribution with a mean of Rs. 750 and a standard deviation of Rs. 50. To find the lowest income among the richest 250, we can use the concept of z-scores.

A z-score tells us how many standard deviations away from the mean a particular data point is. We can calculate the z-score for the 250th highest income using the formula:

z = (x - mean) / standard deviation

Plugging in the values, we get:

z = (x - 750) / 50

Since we want the lowest income among the richest 250 individuals, we are looking for the value of x when z = -1.645 (which is the z-score corresponding to the top 2.5% of the distribution).

Rearranging the formula, we have:

x = -1.645 * 50 + 750 = Rs. 675.75

Therefore, the lowest income among the richest 250 is Rs. 675.75.