Question

a population has a mean of 200 and a standard deviation of 50. a sample of 100 observations will be taken. the probability that the sample mean will be between 190 to 210 is

Answer 1

The probability that the sample mean is between 190 and 210 using the Zscore distribution principle is 0.9545

Given the Parameters :

• Mean, μ = 200
• Standard deviation, σ = 50

Standard Error = σ/√n

Standard Error(S.E) = 50/√100 = 5

Zscore = (x - μ) ÷ S.E

At score, x = 210 ;

• Zscore = (210 - 200) ÷ 5 = 2

At score, x = 210 ;

• Zscore = (190 - 200) ÷ 5 = - 2

P(Z < 2) - P(Z < - 2) = 0.97725 - 0.02275

P(Z < 2) - P(Z < - 2) = 0.9545

Therefore, the probability that sample mean is between 190 to 210 is 0.9545

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