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Consider independent random variables Zi ∼ N(0, 1), i = 1, …, 16, and let Z be the sample mean. Find:
a) P[Zbar <1/ 2].
b) P[Z1 − Z2 < 2].
c)P[Z1 + Z2 <2].
Assume that Z, V1 and V2 are independent random variables with Z ~ N(0,1), V1 ~ X^2 (5) (chi-square) and V2 ~ X^2 (9) (chi-square). Find the following:
a) P[V1+V2<8.6]
b)P[Z/(sqrt(V1/5))<2.015]
c)P[Z> 0.611(sqrt(V2))]
d)P[V1/V2 < 1.450]
e)The value b such that P[V1/(V1+V2) < b] = 0.90.
S denotes the diameter of a shaft and B the diameter of a bearing, where S and B are
independent with S distrubbute N(1, 0.0004) and B distrubute N(1.01, 0.0009).
(a) Ifa shaft and a bearing are selected at random, what is the probability that the shaft
diameter will exceed the bearing diameter?
(b) Assume equal variances σ1^2=σ2^2=σ^2 , and find the value of σ that will yield a probability of noninterference of 0.95.
on a recent math test , the mean score was 75 and the standard deviation was 5. mike got 85. what percentile does he fall in?
a line up for tickets to a local concert had an average waiting time of 20 minutes with a standard deviation of 4 minutes
a. what percentage of the people in line waited for more then 20 minutes
There are 12 students who will be taking up the test, the researcher sets the level
of significance to 0.10. The following are the scores of the nine students:
23, 25, 25, 26, 27, 28, 30, 40, 45, 46, 48, 53
A random of 25 sample is drawn from a population with sample mean 105.2 and standard deviation 11.13 Construct a 90% confidence interval. *
Provide step-by-step solutions to the given problem below. Write your answers on
the spaces provided.
Consider all samples of size 2 from the population 2, 5, 6, 9, 11, and 13. Compute
the mean, and variance of the sampling distribution of the sample mean.
First step:
Second step
a)
b)
Third step
Fourth step
Fifth step
Sixth step
a)
b)
Seventh step
a)
b)
c)
d)
If the sample mean is 75 and the sample standard deviation is 5.Find the corresponding standard deviation of the score 70
Use formula to find z score z=x–x/ó
Use the Standard normal Curve to answer the following,On the first periodic exam in statistics,the population mean was 70 and the standard deviation was 9.Determine the standard score of the student who got a score of 88 assuming the score was normally distributed.
#340153 on Dec 2023