Answer to Question #113711 in Statistics and Probability for Katenda

Question

QUESTIONS 16 TO 19 ARE BASED ON THE FOLLOWING INFORMATION.

A Check uses AI algorithm to detect FN. The number of times the algorithm is successful at detecting FN is normally distributed with the mean of 1000 and the standard deviation of 100. Let X be the number of times the algorithm is successful at detecting FN.

Question 16

Choose the incorrect

The probability that X is at most
(1) 800 is 0.0228
(2) 900 is 0.1587
(3) 1000 is 0.0000
(4) 1100 is 0.8413
(5) 1200 is 0.9772

Question 17

What is the probability that X is at least 950?

(1) 0.6915
(2) 0.5000
(3) 0.3085
(4) 0.0000
(5) None of the above

Question 18

What is the probability that X is between 1000 and 1300?

(1) 0.9990
(2) 0.9987
(3) 0.5000
(4) 0.4987
(5) 0.0000

Question 19

A Check knows that the probability that X is at most x is 0.8997 i.e. P(X ≤ x) = 0.8997. What is the value of x?

(1) 1.2
(2) 1.28
(3) 1120
(4) 1128
(5) None of the above

Answer 1

16) (3) 1000 is 0.0000  - incorrect because 1000 is the mean value

17) (1) 0.6915 

P(x>950)=1-P(x<950)

z=(950-1000)/100=-0.5, using table - P(x<950)=0.3085

P(x>950)=1-0.3085= 0.6915 

18) (4) 0.4987

P(1000<x<1300)=P(x<1300)-P(x<1000)

P(x<1300). z=(1300-1000)/100=3, using table P(x<1300)=0.9987

P(x<1000). z=(1000-1000)/100=0, using table P(x<1000)=0.5

P=0.9987-0.5=0.4987

19)(4) 1128 

P(X ≤ x) = 0.8997

using table - z-value(0.8997)=1.28

(x-1000)/100=1.28

x=1.28*100+1000=1128