Asked Jul 29, 2019

Given a standardized normal distrubtion (with a mean of 0 and a standard deviation of 1, as in Table E.2) what is the probability that

a. Z is less than 1.57?

b. Z  is greater than 1.84?

c. Z is between 1.57 and 1.84?

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


Expert Answer

Step 1

Standard normal distribution:

The standard normal distribution is a special case of normal distribution, in which the mean of the distribution is 0 and standard deviation of the distribution is 1. The Z-scores can be calculated using the given formula.


Image Transcriptionclose

х— и where, x is the normal random variable is the mean, and g is the standard deviation

Step 2

a. Probability of Z is less than 1.57:

The probability of Z is less than 1.57 is found to be 0.9418 from the calculation given below.


Image Transcriptionclose

using EXCEL formula, "=NORM.S.DIST(1.57,TRUE)" P(z<1.57) 0.9418

Step 3

b. Probability of Z is greater than 1.84:

The probability of Z is greater than 1.84 is fou...


Image Transcriptionclose

P(z>1.84) 1-P(z <1.84) [using EXCEL formula, NORM.S.DIST(1.84,TRUE)" 1-0.9671 0.0329


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