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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.
a. for the top and bottom of the box costs P30 per square centimeter and the material for the sides cost P15 per square centimeter. Find the dimensions of the box so that the total cost of material is the least possible and all its dimensions do not exceed 20cm.
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
A 9.0m ladder rest against the side of a wall. The bottom of the ladder is 1.5m from the base of the wall. Determine the measure of the angle between the ladder and the ground.
Calculate z^6=64
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
Form the partial differential equation by eliminating the arbitrary constants a and b from z = xy + y((x+a) ^1/2) + b
#339914 on Dec 2023