What is the z-score of x = -2, if it is 2.78 standard deviations to the left of
ID: 3324746 • Letter: W
Question
What is the z-score of x = -2, if it is 2.78 standard deviations to the left of the mean?
Less than 0
1.6 – 2.5
0 – 0.5
More than 2.5
0.6 – 1.5
11) Suppose a normal distribution has a mean of six and a standard deviation of 1.5. What is the z-score if x = 5.5? Save your answer, as you’ll need it for the next two questions.
1.6 – 2.5
0 – 0.5
0.6 – 1.5
Less than 0
More than 2.5
12) For the z score you just calculated, what’s the corresponding p value? This p value measures the percent of the area under the curve to the left of z. Hint: draw a diagram.
0% – 20%
20% – 40%
40% - 60%
60% - 80%
80% - 100%
13) And based on the z score you calculated for question 11, what’s the percent of the area to the right of z.
0% – 20%
20% – 40%
40% - 60%
60% - 80%
80% - 100%
14) In a normal distribution, x = 5 while the z score = –1.25. This tells you that x = 5 is ____ standard deviations to the ____ (right or left) of the mean.
5, right
1.25, right
5, left
1.25, left
15) If the area to the right of x in a normal distribution is .243, what is the area to the left of x?
Less than 0.45
0.56 – 0.65
More than 0.75
0.45 – 0.55
0.66 – 0.75
16) Christmas trees can be recycled by feeding them to goats. Assume that the number of trees a goat can eat is normally distributed. The mean goat can eat 20 trees an hour, with a standard deviation of 2 trees. Sixty-eight percent of the time, how many trees can a goat consume?
19-21
Exactly 20
10-30
15-25
18-22
17) Christmas trees can be recycled by feeding them to goats. Assume that the number of trees a goat can eat is normally distributed. The mean goat can eat 20 trees an hour, with a standard deviation of 2 trees. What percent of the time will a goat consume between 16 and 24 Xmas trees?
50%
0%
99.7%
95%
68%
18) The average professor nods off at his desk 384 times in any given year, with a standard deviation of 50 nods. Assume that nods are normally distributed (I assume it because I made all this up). What’s the probability that a professor nods off less than 250 times?
0.16 – 0.25
More than 0.35
0.05 – 0.15
0.26 – 0.35
Less than 0.05
19) The average professor nods off at his desk 384 times in any given year, with a standard deviation of 50 nods. Assume that nods are normally distributed (I assume it because I made all this up). What’s the probability that a professor nods off less than 420 times?
More than 0.85
0.66 – 0.75
0.76 – 0.85
0.55 – 0.65
Less than 0.55
20) The average professor nods off at his desk 384 times in any given year, with a standard deviation of 50 nods. Assume that nods are normally distributed (I assume it because I made all this up). What’s the probability that a professor nods off more than 420 times?
Less than 0.05
0.16 – 0.25
More than 0.35
0.05 – 0.15
0.26 – 0.35
21) The average professor nods off at his desk 384 times in any given year, with a standard deviation of 50 nods. Assume that nods are normally distributed (I assume it because I made all this up). What’s the probability that a professor nods off more than 1,000,000 times?
Less than 0.05
0.05-0.15
More than 0.35
0.26 – 0.35
0.16 – 0.25
Explanation / Answer
Q10) Option A is Correct. Less than zero, because it lies to the left of mean
Q11) Option D is Correct. Less than zero
z = (5.5-6)/1.5
z = -0.33
Q12) p value = P(z<-0.33)
P value = 0.3694
So, 20%-40%
Option B is Correct
Q13) Area to right of z = 1-0.3694 = 0.6306
60%-80%
Option D is Correct
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