Name:1) Consider a binomial experiment with n = 20 trials and p = 0.40.a) Find the expected value and the standard deviation of the distribution.MAT 147: StatisticsHW 7: More Binomial Distribution0.38b) It is unusual for a binomial experiment to have values that are more than 2 standard deviationsaway from the mean. Would it be unusual to obtain fewer than 3 successes? Explain.2) The quality-control inspector of a production plant will reject a bath of syringes if two ormore defective syringes found in a random sample of eight syringes taken from the batch.Suppose the batch contains 1% (0.01) defective syringes.b) Find u. What is the expected number of defective syringes the inspector will find?Intervald) Find o.c) What is the probability that the batch will be accepted? Find the probability of 0 or 1defective syringes.Cluster sampl

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A psychologist finds that fidgety patients tap their fingers on average 500 times during a 2 hour period. You wish to test this claim for the same patients, but in a room decorated with soothing colors and soft lighting. You believe that a warmly decorated room may alter the fidgeting behavior, causing subjects to tap their fingers less than they do under normal conditions. A random sample of 400 patients has a mean of 420 taps and a standard error of 30 taps in a 2 hour period. Find the margin of error for the average tapping of fingers during a 2 hour period.
Show neat and complete solution. (... The average fuel efficiency of U.S. light vehicles (cars, SUVs, minivans, vans, and light trucks) for 2005 was 21 miles per gallon (mpg). If the standard deviation of the population was 2.8 and the gas ratings were normally distributed, (a) what is the probability that the mean mpg for a random sample of 25 light vehicles is under 18? (b) between 20 and 24? Given: Required: Solution: a. b.
4. Manufacturer A's television picture tubes have a mean lifespan of 7.3 years and a standard deviation of 0.57 years; while those of manufacturer B have a mean duration of 6.39 years and a standard deviation of 0.42 years. What is the probability that a random sample of 39 kinescopes from manufacturer A will have a mean lifespan that is 1 year less than the mean lifespan in a sample of 43 kinescopes from manufacturer B? Round your answer to four decimal places after the period.
An automobile battery manufacturer claims that its mid grade battery has a mean life of 50 months with a standard deviation of 6 months Suppose the distribution of battery lives of this particular brand is approximately normal. Find the probability that the mean of a random sample of 36 such batteries will be less than 48 months. Is the assumption of the manufacturers' claims true? Why?
The manager of a restaurant believes that waiters and waitresses who introduce themselves by telling customers their names will get larger tips than those who don't. In fact, she claims that the average tip for the former group is 17% while that of the latter is only 12%. If tips are normally distributed with a standard deviation of 9%. what is the probability that in a random sample of 13 tips recorded from waiters and waitresses who introduce themselves and 13 tips from waiters and waitresses who don't, the mean of the former will exceed that of the latter? Probability =
Two independent random samples of sizes 8 and 7 gave variances 4.2 and 3.9 respectively. Do you think that such a difference has probability less than 0.05? Justify your answer.
2) A restaurant association claims that the average amount a family spends per year eating out is $2700. Suppose you are a consumer reporter and want to test this claim. You select a random sample of 32 homes and obtain that their mean is $2850 with a standard deviation of $270. using α= 0.05, do you have enough evidence to reject the association's claim?
4. Past experience indicates that the time required for high school seniors to complete a standardized examination is a normal random variable with a mean of 35 minutes. If a random sample of 20 high school seniors took an average of 33.1 minutes to complete the examination with a standard deviation of 4.3 minutes, test the hypothesis at 5% level of significance that µ = 35 minutes, against the alternative µ< 35 minutes.
5. One roll of a 'fair' six-sided die has an expected value or mean of 3.5 with a variance of 2.92. Suppose you plan to roll a die 60 times and compute the mean value in an effort to determine whether it is a fair die. (Fair in this case means that each of the six sides has an equal probability of being the roll value.) a. Use a z value of 1.85 to compute an interval around a fair die's population mean that can be compared to the mean of the 60 rolls of the potentially fair or unfair die if the mean of the sample is 3.3. b. When a z value of 1.85 is used to compute a confidence interval around an unfair die's sample mean from 60 rolls, what is the confidence level for the interval?
Suppose a researcher pbserves a population of 12 people and computes SS=204. What is the variance? What is the standard deviation?
4. Manufacturer A's television picture tubes have a mean lifespan of 7.23 years and a standard deviation of 0.72 years; while those of manufacturer B have a mean duration of 6.46 years and a standard deviation of 0.44 years. What is the probability that a random sample of 38 kinescopes from manufacturer A will have a mean lifespan that is 1 year less than the mean lifespan in a sample of 42 kinescopes from manufacturer B? Round your answer to four decimal places after the period.

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