Give Example Of Central Limit Theorem?

1.	Give Example Of Central Limit Theorem?
Answer» Given that the population of men has NORMALLY distributed weights, with a mean of 173 lb and a standard deviation of 30 lb, find the probability that a. if 1 MAN is randomly selected, his weight is greater than 180 lb. b. if 36 different men are randomly selected, their mean weight is greater that 180 lb. SOLUTION: a) Z = (X - μ)/ σ = (180-173)/30 = 0.23 For normal distribution P(Z>0.23) = 0.4090 b) σ x̄ = σ/√n = 20/√ 36 = 5 z= (180-173)/5 = 1.40 P(Z>1.4) = 0.0808 Given that the population of men has normally distributed weights, with a mean of 173 lb and a standard deviation of 30 lb, find the probability that a. if 1 man is randomly selected, his weight is greater than 180 lb. b. if 36 different men are randomly selected, their mean weight is greater that 180 lb. Solution: a) z = (x - μ)/ σ = (180-173)/30 = 0.23 For normal distribution P(Z>0.23) = 0.4090 b) σ x̄ = σ/√n = 20/√ 36 = 5 z= (180-173)/5 = 1.40 P(Z>1.4) = 0.0808

Answer»

Given that the population of men has NORMALLY distributed weights, with a mean of 173 lb and a standard deviation of 30 lb, find the probability that

a. if 1 MAN is randomly selected, his weight is greater than 180 lb.

b. if 36 different men are randomly selected, their mean weight is greater that 180 lb.

SOLUTION: a) Z = (X - μ)/ σ = (180-173)/30 = 0.23

For normal distribution P(Z>0.23) = 0.4090

b) σ x̄ = σ/√n = 20/√ 36 = 5

z= (180-173)/5 = 1.40

P(Z>1.4) = 0.0808

Given that the population of men has normally distributed weights, with a mean of 173 lb and a standard deviation of 30 lb, find the probability that

a. if 1 man is randomly selected, his weight is greater than 180 lb.

b. if 36 different men are randomly selected, their mean weight is greater that 180 lb.

Solution: a) z = (x - μ)/ σ = (180-173)/30 = 0.23

For normal distribution P(Z>0.23) = 0.4090

b) σ x̄ = σ/√n = 20/√ 36 = 5

z= (180-173)/5 = 1.40

P(Z>1.4) = 0.0808

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