Given a standardized normal distribution (with a mean of 0 and a standard deviat

Question

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

a.   What is the probability that Z is between -1.55 and 1.86?

The probability that Z is between -1.55 and 1.86 is 0.9080

b.   What is the probability that Z is less than -1.55 or greater than 1. 86?

The probability that Z is less than -1.55 or greater than 1.86 is 0.0920.

c.    What is the value of Z if only 1% of all possible Z values are larger?

The value of Z if only 1% of all possible Z values are larger is 2.3263.

d.   Between what two values of Z (symmetrically distributed around the mean) will 98.36% of all possible Z values be contained?

The two values of Z for which 98.36% of all possible Z values are contained between are ____ and _____. (please show work so I can know how to get the answer on my own)

Explanation / Answer

a) P(-1.55<z<1.86)

Use excel function NORMSDIST(1.86)-NORMSDIST(-1.55)

= 0.9080 (rounded to four decimal places)

B) P(z<-1.55)+p(z>1.86)

Use excel function

NORMSDIST(-1.55)+(1-NORMSDIST(1.86))

= 0.0920 (rounded to four decimal places)

c) Use

NORMSINV(0.99)

= 2.3263

d) Use

NORMSINV(0.9836+(0.0164/2)) = 2.4

So, two z values are -2.4 to 2.4

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