Normal distribution

6. Given a standard normal distribution [with mean 0 and standard deviation 1], answer the following:

(a) What is the probability that

a. Z is less than 1.57?

b. Z exceeds 1.84?

c. Z is between 1.57 and 1.84?

d. Z is less than 1.57 or greater than 1.84?

e. Z is between - 1.57 and 1.84?

f. Z is less than - 1.57 or greater than 1.84?

(b) What is the value of Z if 50% of all possible values of Z are greater?

(c) What is the value of Z if only 2.5% of all possible values of Z are greater?

(d) Between which two values of Z (symmetric around the mean) will 68.26% of all possible values of Z be contained?

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