Question

a)Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)

The area between

z = 1.34 and z = 2.29 is

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

P(z ≤ −2.14)=
Shade the corresponding area under the standard normal curve.

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

P(z ≥ −1.58) =
Shade the corresponding area under the standard normal curve.

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

P(−2.05 ≤ z ≤ 1.15)=
Shade the corresponding area under the standard normal curve.

Answer 1

Solution :

Given that,  

Using standard normal table ,

a)

P(1.34 < z < 2.29)

= P(z < 2.29) - P(z < 1.34)

= 0.989 - 0.9099

= 0.0791

P(1.34 < z < 2.29) = 0.0791

b)

P(z -2.14) = 0.0162

c)

P(z -1.58) = 1 - P(z -1.58) = 1 - 0.0571 = 0.9429

d)

P(-2.05 z 1.15)

= P(z 1.15) - P(z -2.05)

= 0.8749 - 0.0202

= 0.8547

P(-2.05 z 1.15) = 0.8547