Question

1. 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 = 6.0; σ = 1.1

P(7 ≤ x ≤ 9) =

2. 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 = 51; σ = 16

P(40 ≤ x ≤ 47) =

Answer 1

Solution :

1.

= P[(7 - 6.0 / 1.1) (x - ) / (9 - 6.0 / 1.1) ]

= P(0.91 z 2.73)

= P(z 2.73) - P(z 0.91)

= 0.9968 - 0.8186

= 0.1782

P(7 x 9) = 0.1782

2.

= P[(40 - 51 / 16) (x - ) / (47 - 51 / 16) ]

= P(-0.69 z -0.25)

= P(z -0.25) - P(z -0.69)

= 0.4013 - 0.2451

= 0.1562

P(40 x 47) = 0.1562