17 Problem Solve
akem_k
stat_17_ps.docxWhich of the functions sketched below could be a probability density function for a continuous random variable?
Your answers.
(a) f
be a probability density function
(b) f
be a probability density function
(c) f
be a probability density function
(d) f
be a probability density function
Find the standardized variable Z if X has
Mean 10 and standard deviation 5.
Your answer:
Z = (X -
) /
·
Find the standardized variable Z if X has
Mean 46 and standard deviation 6.
Your answer:
Z = (X -
) /
·
Find the area under the standard normal curve to the right of
z = 1.35
Round your answer to four decimal places.
Your answer:
P [Z > 1.35] =
Warning
|
|
the absolute tolerance is +/-0.0001
Find the area under the standard normal curve to the right of:
z = -1.10
Round your answer to four decimal places.
Your answer:
P [Z > -1.10] =
Find the area under the standard normal curve over the interval z = −0.39 to z = 0.39. Compute probabilities using the standard normal table in Appendix B (Table 3) . Round the answer to four decimal places.
Area = .
Find the area under the standard normal curve over the interval z = 0.42 to z = 2.39. Compute probabilities using the standard normal table in Appendix B (Table 3) . Round the answer to four decimal places.
Area = .
For a standard normal random variable Z, find P[− 1.5 < z < 2.50]. Compute probabilities using the standard normal table in Appendix B (Table 3) . Round the answer to four decimal places.
P[− 1.5 < z < 2.50] =
.
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.
·
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 390 and 740.0.
Round your answer to four decimal places.
Your answer.
·
A population has mean 52 and standard deviation 11. Calculate for a random sample of size 20.
·
· A population has mean 33 and standard deviation 12. Calculate for a random sample of size 11.
·
· (Round to one decimal place.)
A population has standard deviation 14. What is the standard deviation of for a random sample of size n = 9?
(Round to one decimal place.)
A population has standard deviation 9. What is the standard deviation of for a random sample of size n = 144?
(Round to one decimal place.)
Suppose the weights of packages of lettuce coming off a packaging line have a normal distribution with mean 8.6 ounces and standard deviation 0.8 ounce. If every package is labeled 10.2 ounces, what proportion of the packages weigh less than the labeled amount?
% (Round to the whole.)
Suppose the weights of the contents of cans of mixed nuts have a normal distribution with mean 32.4 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.
· %
The number of complaints per day, X, received by a cable TV distributor has the probability distribution
|
X |
0 |
1 |
2 |
3 |
|
f(X) |
0.5 |
0.3 |
0.1 |
0.1 |
Find the expected number of complaints per day.
