Answers are in BLUE
Find the standardized variable Z if X has
Mean 48 and standard deviation 9.
Your answer:
Z = (X - ) /
Open Show Work
Answer: 𝑍 =
𝑋−48
9
Find the standardized variable Z if X has
Mean 157 and variance 36.
Your answer:
Z = (X - ) /
Answer: 𝑍 =
𝑋−157
6
Find the area under the standard normal curve to the right of
z = 0.15
Round your answer to four decimal places.
Your answer: P [Z > 0.15] = 0.4404
the absolute tolerance is +/-0.0001
Find the area under the standard normal curve to the right of
z = 0.20
Round your answer to four decimal places.
Your answer:
P [Z > 0.20] = 0.4207
the absolute tolerance is +/-0.0001
Find the area under the standard normal curve over the interval z = −0.22 to z = 0.22. Compute
probabilities using the standard normal table in Appendix B (Table 3). Round the answer to
four decimal places.
Area = 0.1741
the absolute tolerance is +/-0.0015
Find the area under the standard normal curve over the interval z = 0.17 to z = 2.29. Compute
probabilities using the standard normal table in Appendix B (Table 3). Round the answer to
four decimal places.
Area = 0.4215
the absolute tolerance is +/-0.0001
For a standard normal random variable Z, find P[− 1.8 < z < 2.21]. Compute probabilities using
the standard normal table in Appendix B (Table 3). Round the answer to four decimal places.
P[− 1.8 < z < 2.21] = 0.9505
Scores on a certain nationwide college entrance examination follow a normal distribution with
a mean of 500 and a standard deviation of 100. Find the probability that a student will score:
Over 610.0.
Round your answer to four decimal places.
Your answer: 0.1357
the absolute tolerance is +/-0.0001
Scores on a certain nationwide college entrance examination follow a normal distribution with
a mean of 550 and a standard deviation of 100. Find the probability that a student will score:
Between 360 and 720.0.
Round your answer to four decimal places.
Your answer. 0.927
the absolute tolerance is +/-0.0001
A population has mean 44 and standard deviation 5.
Calculate for a random sample of size 17. Which is the question here?
Suppose the weights of packages of lettuce coming off a packaging line have a normal
distribution with mean 8.2 ounces and standard deviation 0.9 ounce. If every package is
labeled 9.1 ounces, what proportion of the packages weigh less than the labeled amount? %
(Round to the whole.)
Answer: 84%
Suppose the weights of the contents of cans of mixed nuts have a normal distribution with
mean 32.2 ounces and standard deviation 0.4 ounce.
If two packages are randomly selected, what is the probability that the average weight is less
than 32 ounces?
Round to one decimal place.
%
Answer: 24.0 %
The number of complaints per day, X, received by a cable TV distributor has the probability
distribution
X0123
f(X) 0.4 0.3 0.1 0.2
Find the expected number of complaints per day.
Answer: 1.1