Question

Part IV: Finding exact probabilities. FOR EACH, DRAW A PICTURE AND USE THE Z-TABLE ON CARMEN.

20. The Z-table always gives you the probability of being between ________ and  the number you are looking up.

21. The number you are looking up should have ______digit(s) before the decimal point and _____ digit(s) after the decimal point.

22. Suppose the Z value is 2.00. Which row and column do you look in to find P(0< Z < 2.00)?

            

23. How do you find P(Z < 2.00)? (Note you have to do this in 2 parts. Hint: What is the probability that Z is less than 0? Use that as one of the parts)

            

24. How do you find P(Z > 2.00)? (Note the table does not have “>” probabilities. If half of the probability is greater than 0, how much of it must be greater than 2? Draw a picture. )

            

25. a. What is P(-1.26  < Z < 0)?  (Note the Z table has no negative values. Use SYMMETRY to do this.)

25.  b.  Find P(Z > -1.26)

25.  c. Find P(Z < -1.26)

26.a   Now find P(-1 < Z < 2). Do this in two parts and sum them together. Use symmetry to get the left part.

26b. Find P(1<Z<2)

Answer 1

(20)- table always gives the probability that Z is less than the specified value, for example:-

P(Z<1)=0.8413.

ie. p(-infinite<Z<1)=0.8413

The Z-table always gives you the probability of being between minus infinite and the number you are looking up.

(21)- z table is given below

hence number should have one digit before decimal and 2 after decimal point.

(22)- here we have to look in row of 2.0 and column of 0.0

(23)- explained above

(24)-(25)- (a)- because by symmetry p(z<0) = 0.50

and p(-1.26<z<0) = p(z<0)-p(z<-1.26)

= 0.50-0.1038

=0.3692

(b)- P(Z > -1.26)= 1-p(z<-1.26)

= 1-0.1038 (calculated above)

= 0.8962

25. c. P(Z < -1.26) = 0.1038

26. a-

probability = p(z<-1)-p(z<2)

= p(z<1)-p(z<2)

hence we get required probability = 0.1587-0.9982

= 0.8185

26.b. similarly p(1<z<2)

= 0.9772-0.8413

= 0.1359

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