Question

Compute the following probabilities using your calculator. Assume Z is a standard normal random variable. Round all answers to three decimal places.

A. P(0<Z<1.85)P(0<Z<1.85)=

B. P(−1.15<Z<0.3)=

C. P(Z>−1.3))=

D. P(0<Z<2.35)=

E. P(−1.85<Z<0.7)=

F. P(Z>−1.2)=

Suppose the random variable xx is best described by a normal distribution with μ=29μ=29 and σ=3.4σ=3.4. Find the zz-score that corresponds to each of the following xx values.

Round answers to three decimal places

(a)  x=16.2
z=

(b)  x=33.4
z=

(c)  x=17.2
z=

(d)  x=38.6
z=

Find the following probabilities for the standard normal random variable z:

Round answers to three decimal places.

(a)  P(z≤2.21)=

(b)  P(z>−2.27)=

Answer 1

Question 1

Part a)

P ( 0 < Z < 1.85 )
P ( Z < 1.85 ) - P ( Z < 0 ) = 0.9678 - 0.5 = 0.468

Part b)

P ( -1.51 < Z < 0.3 ) = P ( Z < 0.3 ) - P ( Z < -1.51 ) = 0.6179 - 0.0655 = 0.552

Part c)

P ( Z > -1.3 ) = 1 - P ( Z < -1.3 ) = 1 - 0.0968 = 0.903

Part d)

P ( 0 < Z < 2.35 ) = P ( Z < 2.35 ) - P ( Z < 0 ) = 0.9906 - 0.5 = 0.491

Part e)

P ( -1.85 < Z < 0.7 ) = P ( Z < 0.7 ) - P ( Z < -1.85 ) = 0.758 - 0.0322 = 0.726

Part f)

P ( Z > -1.2 ) = 1 - P ( Z < -1.2 ) = 1 - 0.1151 = 0.885

Question 2

Part a)

Z = ( 16.2 - 29 ) / 3.4
Z = -3.76

Part b)

Z = ( 33.4 - 29 ) / 3.4
Z = 1.29

Part c)

Z = ( 17.2 - 29 ) / 3.4
Z = -3.47

Part d)

Z = ( 38.6 - 29 ) / 3.4
Z = 2.82

Question 3

Part a)

P(z≤2.21) =   P ( Z >= 2.21 ) = 1 - P ( Z < 2.21 ) = 1 - 0.9864 = 0.014

Part b)

P(z>−2.27) =   P ( Z > -2.27 ) = 1 - P ( Z < -2.27 ) = 1 - 0.0116 = 0.988