The income of a group of 10000 persons was found to be normally distributed with mean Rs.750 per month?

Question

The income of a group of 10000 persons was found to be normally distributed with mean Rs.750 per month and standard deviation equal to Rs. 50 show that of this group 95% had income exceeding Rs. 668 and only 5% had income exceeding Rs. 832.

Answer 1

P((x - μ)/σ > - 1.6449) = 95%

P(x - μ > - 1.6449σ) = 95%

P(x > μ - 1.6449σ) = 95%

P(x > 750 - 1.6449(50)) = 95%

P(x > 667.755) = 95%

P(x > 668) ≈ 95%

P((x - μ)/σ > 1.6449) = 5%

P(x - μ > + 1.6449σ) = 5%

P(x > μ + 1.6449σ) = 5%

P(x > 750 + 1.6449(50)) = 5%

P(x > 832.245) = 5%

P(x > 832) ≈ 5%