Question

For a normal population with μ = 40 and σ = 10, which of the following samples has the highest probability of being obtained?

		M = 38 for a sample of n = 4
		M = 36 for a sample of n = 4
		M = 38 for a sample of n = 100
		M = 36 for a sample of n = 100

Answer 1

Solution :

Given that ,

mean = = 40

standard deviation = = 10

n = 4

M = 40 and

M = / n = 10 / 4 = 5

P(M < 36) = P((M - M ) / M < (36 - 40) / 5)

= P(z < -0.8)

Using standard normal table,

Probability = 0.2119

M = 38 for a sample of n = 4  has the highest frequency .