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a manufacturer wants to build a spring that takes a force 10 N(in negative direction) to compress it 0.2 m from the equilibrium position.The spring should be able to stretch 0.5 m from the equilibrium position.
as a mechanical engineer, you were asked to present how much work should be done to stretch the spring.the presentationshall include important components of the problems, complete and correct computations and a logical and organizedexplanation.
Find the mean of the probability distribution of the random variable X if P(X) = (2X-1)/10 for X=1,2,3,4, and 5
The arrival rates of telephone calls at telephone booth are according to poisson distribution with
an average time of 12 minutes between arrival of two consecutive calls. The length of telephone
calls is assumed to be exponentially distributed with mean 4 minutes. (1) Determine the
probability that the person arriving at the booth will have to wait. (2) Find the average queue
length that is formed from time to time. (3) The telephone company will install the second booth
when convinced that an arrival would expect to wait atleast 5 minutes for the phone. Find the
increase in flows of arrivals which will justify the second booth. (4) What is the probability that
an arrival will have to wait for more than 15 minutes before the phone is free?
An experiment has been conducted to study the effects of smiling on leniency in judging students accused of cheating. The figure below shows a dotplot of a randomization distribution of differences in sample means.
The relevant hypotheses are H0: μs=μn vs. Ha: μs >μn, where μs and μn are the mean leniency scores for smiling and neutral expressions, respectively. This distribution is reasonably bell-shaped and we estimate the standard error of the differences in means under the null hypothesis to be about 0.393. For the actual sample in Smiles, the original difference in the sample means is 4.91–4.12 = 0.79. Use a normal distribution to find and interpret a p-value for this test.
- What is the standardized test statistic? Round your answer to two decimal places.
- Z =
- What is the p-value? Round your answer to three decimal places.
- p-value =
From a box containing 4 black balls and 2 green balls, 3 balls are drawn in succession Each ball is placed back in the box before the next draw is made. Let G be a random variable representing the number of green balls that occur. Find the values of the random variable G.
In a tennis match, with the score at deuce, the game is won by the first player who gets a clear lead of two points.If the probability that given player wins a particular point isθ, and all points are played independently, what is the probability that player eventually wins the game
The mean time taken by all participants to run a road race was found to be 200 minutes with a
standard deviation of 20 minutes.c. Using the Empirical rule, find the percentage of the runners who ran this road race
completed in-
I. 150 to 250 minutes
II. 110 to 290 minutes
d. Using Empirical rule, find the interval that contains the times taken by at least 99.7% of
all the runners who ran in this road race.
.
A shipment of 9 printers contains 3 that are defective. Find the probability that a sample of size 3, drawn from the 9, will not contain a defective printer.
In a club with 6 male and 13 female members, a 4-member committee will be randomly chosen. Find the probability that the committee contains at least 3 women.
Random samples of size 3 are drawn from a finite population consisting of the numbers 5, 6, 7, 8, 9 and 10.
