Information: Random variable Z represents the number of successes observed in 50
ID: 3235945 • Letter: I
Question
Information: Random variable Z represents the number of successes observed in 500 repetitions of an experiment that has a probability of success of .4 (i.e. the chance of success is 40% for each of the 500 independent experiments). Using this information, determine the following values for the next 5 questions:
Question 5
P(Z = 240), in other words, the probability that there were EXACTLY 240 successes in the 500 trials (round your answer to 2 decimal places):
Select one:
a. .00
b. .01
c. .03
d. .13
e. .53
Question 6
P(Z 240), in other words, the probability that Z is less than or equal to 240 (rounded to two decimal places) is:
Select one:
a. .00
b. .48
c. .62
d. .97
e. 1.00
Question 7
P(220 Z 260) is (choose the best answer):
Select one:
a. .04
b. .13
c. .75
d. .86
e. .91
Question 8
The expected number of successes (the expectation) is:
Select one:
a. 0
b. sqrt( sum(Z – 300)^2 / 500)
c. 200
d. 240
e. 260
Question 9
The population standard deviation of Z is:
Select one:
a. 300 ± 1.683 * z
b. 10.95
c. 12.00
d. 30.00
Explanation / Answer
n =500 , p = 0.40
mean = n p = 500 * 0.40 = 200
std.deviation = sqrt ( npq)
= sqrt ( 0.40 * 200 * 0.6)
= 10.95
6) P(Z < = 240)
z = ( x - mean) / s
= ( 240 - 200) / 10.95
= 3.651
P(x < 240) = P( Z < 21.9089) = 0.99 = 1
Answer is option e)
7)
P(220 Z 260)
P(X < 220)
z = ( x - mean) / s
= ( 220 - 200) / 10.95
= 1.825
P(X < 260)
z = ( x - mean) / s
= ( 260 - 200) / 10.95
= 5.477
P(220 Z 260) = P( 1.825 < z < 5.477) = 0.0339 = 0.4
Answwer is option a)
8)
mean = 200
answer is option c)
9) std. deviation = 10.95
answer is option b)