1.) Find the two standard scores ( z ) that correspond to the following. (Enter

Question

1.) Find the two standard scores (z) that correspond to the following. (Enter your answers from smallest to largest. Give your answers correct to two decimal places.)

(a) The middle 79% of a normal distribution is bounded by them.
(b) The middle 90% of a normal distribution is bounded by them.

2.) Find z, given the following. (Give your answer correct to two decimal places.)

x = 60, = 45 and = 5.5

z = ______

3.) Find z, given the following. (Give your answer correct to two decimal places.)

x = 250, = 222 and = 12.6

z = ____

Explanation / Answer

1) a) P(-z < Z < z) = 0.79

or, P(Z < z) - P(Z < - z) = 0.79

or, P(Z < z) - (1 - P(Z < z)) = 0.79

or, 2*P(Z < z) - 1 = 0.79

or, P(Z < z) = 0.895

or, z = 1.25

So, The middle 79% of a normal distribution is bounded by -1.25 and 1.25.

b) P(-z < Z < z) = 0.90

or, P(Z < z) - P(Z < - z) = 0.90

or, P(Z < z) - (1 - P(Z < z)) = 0.90

or, 2*P(Z < z) - 1 = 0.90

or, P(Z < z) = 0.95

or, z = 1.64

So, The middle 79% of a normal distribution is bounded by -1.64 and 1.64.

2) Z = (X - ) / = (60 - 45) / 5.5 = 2.73

3) Z = (X - ) / = (250 - 222) / 12.6 = 2.22

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