Question

Given a standardized normal distribution​ (with a mean of 0 and a standard deviation of​ 1), complete parts​ (a) through​ (d).

a. What is the probability that Z is less than 1.56? (Round to four decimal places as needed)

b. What is the probability that Z is greater than 1.81? (Round to four decimal places as needed)

c. What is the probability that Z is between 1.56 and 1.81 is (Round to four decimal places as needed)

d. The probability that Z is less than 1.56 or greater than 1.81 (Round to four decimal places as needed)

Answer 1

Solution :

Given that ,

mean = = 0

standard deviation = = 1

a)

= P(z < 1.56)

= 0.9410 Using standard normal table,

Probability = 0.941

b)

P(z > 1.81)

= 1 - P(z < 1.81)

= 1 - 0.9650 Using standard normal table.

= 0.0350

Probability = 0.0350

c)

= P(1.56 < z < 1.81)

= P(z < 1.81) - P(z < 1.56)

= 0.9650 - 0.9410

Probability = 0.0240

d)

P(z < 1.56 or z > 1.81)

= P(z < 1.56) + P(z > 1.81)

= P(z < 1.56) + ( 1 - P(z < 1.81) )

= 0.9410 + ( 1 - 0.9650)

= 0.9410 + 0.0350

= 0.9060