Question

a) Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

P(−2.02 ≤ z ≤ −0.31) =

Shade the corresponding area under the standard normal curve.

b) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 50; σ = 15

P(40 ≤ x ≤ 47) =

c) Find z such that 88.3% of the standard normal curve lies to the left of z. (Round your answer to two decimal places.)
z =

Sketch the area described.

d) Find z such that 8% of the standard normal curve lies to the right of z. (Round your answer to two decimal places.)
z =

Sketch the area described.

Answer 1

Solution

a ) P ( -2.02 < Z < -0.31 )

P ( Z <   -0.31 ) - P ( Z < -2.02 )

=0.3783 - 0.0217

=0.3566

Probability = 0.3566

b ) Given that,

mean = = 50

standard deviation = = 15

P (40 x 47 )

P ( 40 - 50 / 15) ( x -  / ) < (47 - 50 / 15)

P ( - 10 / 15 z - 7 / 15 )

P (-0.67 z - 0.47)

P ( z - 0.47 ) - P ( z -0.67)

Using z table

= 0.3192 - 0.2514

= 0.0678

Probability = 0.0678

c ) P(Z < z) = 88.3%

P(Z < z ) = 0.883

z = 1.19

d ) P ( Z > z ) = 0.08

1 - P ( Z <  z ) = 0.08

P ( Z <  z ) = 1 - 0.08

P ( Z < 1.405 ) = 0.92

z =1.40