Question

A random sample is drawn from a normally distributed population with mean μ = 18 and standard deviation σ = 2.3. [You may find it useful to reference the z table.]

b. Calculate the probabilities that the sample mean is less than 18.6 for both sample sizes. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

	n Probability 26 52

Answer 1

Solution :

Given that ,

mean = = 18

standard deviation = = 2.3

a)

n = 26

= 18

= / n = 2.3 / 26 = 0.4511

P( < 18.6) = P[ - / < 18.6 - 18) /0.4511]

                  = P(z < 1.33)

Using standard normal table,

P( < 18.6) = 0.9082

Probability = 0.9082

b)

n = 52

= 18

= / n = 2.3 / 52 = 0.3190

P( < 18.6) = P[ - / < 18.6 - 18) /0.3190]

                  = P(z < 1.88)

Using standard normal table,

P( < 18.6) = 0.9699

Probability = 0.9699