Score: 0.4 of 1 pt 6.2.2 1017(7 complete) Given a standardized normal distibutio

Question

Score: 0.4 of 1 pt 6.2.2 1017(7 complete) Given a standardized normal distibution (with a mean of 0 and a standard deviation of 1), complete parts (a) through (d) below of a. What is the probability that Z is between -1.52 and 1.87 The probability that Z is between -1.52 and 187 is 9050 Round to four decimal places as needed ) b. What is the probability that Z is less than -1.52 or greater than 1.87? The probability that Z is less than -1.52 or greater than 1.87 is 0850 Round to four decirnal places as needed ) c. What is te value of Z ifonly 4% of all possable Z values are larger? The value ot Z if only 4% of all possible Z values are larger is:175 Round to two decimal places as needed) d Between what two values of Z (symmetrically distributed around the mean) wl' 9g 78% of all possble Z values be co tared? The two valuesofZfor which 98 76% of all possbleZvales are cortared between aed»d (Use ascending order. Round to two decimal places as needed ) Enter your answer in the edit fields and then click Check Answer All parts showing Clear Al lege.com

Explanation / Answer

A) What is the probability that Z is between -1.52 and 1.87?

First we should spilt the values -1.52 into -1.5 & 0.02

Then in the following table find the row -1.52 & find the cloumn 0.02

Similarly for the value of 1.87 as 1.8 & 0.07

Therefore value of Z for -1.52 is 0.0643 and for 1.87 is 0.9693

To find the probability between -1.52 & 1.87 we substract 0.0643 from 0.9693

We get 0.905

Therefore The P(Z is between -1.52 & 1.87) is 0.905.

B) What is the probability that Z is less than -1.52 or greater than 1.87?

P(Z<-1.52) + P(Z> 1.87) = P(Z < -1.52) + (1 - P( Z < 1.87) = 0.0643 + (1 - 0.9693) = 0.095

The probability that Z is less than -1.52 or greater than 1.87 is 0.095.

C) What is the value of Z if only 4% of all possible Z values are larger?

4% means 0.04 possible values of Z are larger then 0.96 are smaller.

So Z = 1.76

D) Between what two values of Z (symmetrically distributed around the mean) will 98.76% of all possible Z values be contained?

If we divide 0.9876 by 2 we get 0.4938. Because the normal curve is symmetrical, half of the 0.4938 will fall below the mean and half will fall above the mean. If we subtract 0.4938 from the 50% i.e 0.5 of the area that is below the mean, we're left with 0.0006 in the tail below the z value you're looking for. We now go to the Standard Normal Table to find the value of z that leaves 0.0006 in the tail.

You look inside the table for the value 0.0006 You then follow the row to the left and the column up to find that the z value is -3.22 Because the normal curve is symmetrical, on the right side of the curve you would have to go to z = +3.22 to leave 0.0006 in the right tail.

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