Question Description
I’m studying for my Engineering class and don’t understand how to answer this. Can you help me study?
- Find the mean and standard deviation of x.
- Using the Binomial Table find the probability that
- Using the Binomial Table find the probability that
- Graph the probability distribution of x, and locate the interval
(b)Using the Binomial Table find the probability that
x £10.
x > 12.
x = 11.
m=± 2s.
Helpful Hints: Find Binomial Probability Table
[Q2] [15 Points]
Suppose we have selected a random sample of n = 36 observation from a population with mean equal to 80 and standard deviation equal to 6. It is known that the population is not extremely skewed.
- Sketch the relative frequency distribution for the population and for the sampling distribution of the sample mean x
Quality Control || Spring 2020 ||
[Q1] [20 Points]
Suppose a poll of 20 voters is taken in a large city. The purpose is to determine x, the number who favor a certain candidate for mayor. Suppose that 60% of all the city’s voters favor the candidate.
(a) Find the mean and standard deviation of x.
(b) Using the Binomial Table find the probability that
(c) Using the Binomial Table find the probability that
(d) Using the Binomial Table find the probability that
x 10.
x 12.
x 11.
(e) Graph the probability distribution of x, and locate the interval
2 .
Helpful Hints: Find Binomial Probability Table
[Q2] [15 Points]
Suppose we have selected a random sample of n = 36 observation from a population with mean equal to 80 and standard deviation equal to 6. It is known that the population is not extremely skewed.
(a) Sketch the relative frequency distribution for the population and for the sampling distribution of the sample mean x
(b) Find the probability that x will be larger than 82.
Helpful Hints: Use the Central Limit Theorem [Q3] [15 Points]
Ecologists often use the number of reported sightings of a rare species of animal to estimate the remaining population size. For example, suppose the number x of reported sightings per week of the blue whales is recorded. Assume that x has (approximately) a Poisson probability distribution. Furthermore, assume that the average number of weekly sightings is 2.6.
(a) Find the mean and standard deviation of x, the number of blue-whale sightings per week.
(b) Using Poisson Probability Table (find your own) calculate the probability that fewer than two sightings are made during a given week.
(c) Using Poisson Probability Table (find your own) find the probability that fewer than two sightings are made during a given week.
Helpful Hints: Use Poisson Probability Table
[Q4] (15 Points)
Given
p0.10 0.053 and
p0.95 0.014, determine the single sampling plan that exactly meets the consumer's
stipulation and comes as close as the possible to the producer's stipulation
[Q5] (15 Points)
The U.S. Army Corps of Engineers has collected data for a random sample of 144 fish contaminated with DDT. (The engineers made sure to capture contaminated fish in several different randomly selected streams and tributaries of the Tennessee River.) The fish weights (in grams) are saved in the FISHDDT file. The Army Corps of Engineers wants to estimate the true variation in fish weights in order to determine whether the fish are stable enough to allow further testing for DDT contaminations.
(a) Us the sample data to find a 95% confidence interval for the parameter of interest
(b) Determine whether the confidence interval in part a is valid?
Helpful Data: MINITAB Descriptive Statistics-(Weight): Mean: 1049.7 and Standard Deviation: 376.5
Helpful Note: Use
2 (chi-square distribution).
[Q6] (10 Points)
The effect of drugs and alcohol on the nervous system has been the subject of considerable research. Suppose a research neurologist is testing the effect of a drug on response time by injecting 100 rats with a unit dose of the drug, subjecting each rat to a neurological stimulus, and recording the response time. The neurologist knows that the mean response time for rats not injected with the drug (the “control” mean) is 1.2 seconds. She wishes to test whether the mean response time for the drug-injected rats different from 1.2 seconds. Set up the test hypothesis for the experiment, using α = 0.01. In other words, do the followings:
(a) What is the Null Hypothesis?
(b) What is the Alternate Hypothesis?
(c) What are the Test Statistics?
(d) What are the Rejection Regions?
[Q7] (10 Points)
"Using Excel" construct the life-history curve for the following test-data:
Test Hours Failures Survivors
0-49 150 350
50-99 80 270
100-149 35 235
150-199 30 205
200-249 25 185
250-299 30 155
300-349 50 105
350-399 60 45
400-449 30 15
450-499 15 0
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