According to a study, 51% of all males between the ages of 18 and 24 live at home. (Unmarried college students living in a dorm are counted as living at home.) Suppose that asurvey is administered and 118 of 206 respondents indicated that they live at home. (a) Use the normal approximation to the binomial to approximate the probability that at least 118respondents live at home. (b) Do the results from part (a) contradict the study?(a) P(X≥ 118)= (Round to four decimal places as needed.)www.

The population proportion is, The sample size is The number of successes is Given that to use the…

Answered: According to a study, 51% of all males…

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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Consider a Bernoulli Experiment with 7 trials. If the expected number of “successful” trials is 4, what is the probability of a “successful trial”? What is the variance of the Binomial Distribution formed ?
If ? is a binomial random variable, compute the mean, the standard deviation, and the variance for each of the following cases: (a) ?=4,?=0.2?=?2= ?= (b) ?=5,?=0.9?= ?2=?=
According to a candy company, packages of a certain candy contain 24% orange candies. Find the approximate probability that the random sample of 300 candies will contain 29% or more orange candies. Using a normal approximation, what is the probability that at least 29% of 300 randomly sampled candies will be orange?
According to a study, 73% of all males between the ages of 18 and 24 live at home. (Unmarried college students living in a dorm are counted as living at home.) Suppose that a survey is administered and 174 of 236 respondents indicated that they live at home. (a) Use the normal approximation to the binomial to approximate the probability that at least 174 respondents live at home. (b) Do the results from part (a) contradict the study? (a) P(X≥ 174) = (Round to four decimal places as needed.)
The president of Doerman Distributors, Inc., believes that 28% of the firm's orders come from first-time customers. A simple random sample of 100 orders will be used to estimate the proportion of first-time customers. What is the probability that the sample proportion will be between 0.16 and 0.40 (to 4 decimals)? What is the probability that the sample proportion will be between 0.21 and 0.35 (to 4 decimals)?
In studies for a medication, 12 percent of patients gained weight as a side effect. Suppose 530 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that (a) exactly 64 patients will gain weight as a side effect. (b) no more than 64 patients will gain weight as a side effect. (c) at least 75 patients will gain weight as a side effect. What does this result suggest?
3. In the Healthy Hand-washing Survey, it was found that 64% of adult Americans operate the flusher of toilets in public restrooms with their foot. Suppose a random sample of n=20 adult Americans is obtained and the number x who flush public toilets with their foot is recorded. (a) Explain why this is a binomial experiment. (b) Find and interpret the probability that exactly 12 flush public toilets with their foot.
Of all the students, 44% own an iPhone, with a standard deviation of .03 For that same sample of 400 students, what is the probability that at least 42% of them own an iPhone?
I. Boston Children’s Hospital estimates that 90% of Americans have had chickenpoxby the time they reach adulthood.32(a) Suppose we take a random sample of 100 American adults. Is the use of the binomial distributionappropriate for calculating the probability that exactly 97 out of 100 randomly sampled Americanadults had chickenpox during childhood? Explain.(b) Calculate the probability that exactly 97 out of 100 randomly sampled American adults had chickenpoxduring childhood.(c) What is the probability that exactly 3 out of a new sample of 100 American adults have not hadchickenpox in their childhood?(d) What is the probability that at least 1 out of 10 randomly sampled American adults have had chickenpox?(e) What is the probability that at most 3 out of 10 randomly sampled American adults have not hadchickenpox?
13 GreenBeam Ltd, claims that its compact fluorescent bulbs average no more than 3.29 mg of mercury. A sample of 25 bulbs shows a mean of 3.36 mg of mercury. (e) State the hypotheses for a right-tailed test, using GreenBeam's claim as the null hypothesis about the mean. a Ha 2329 mg vs. H u329 mg c H =329 mg vs. H p+3.29 mg eBook Hirt sterences (b) Assuming e known standerd deviation of 0.21 mg, calculate the z test statistic to test the manufacturer's claim. (Round your answer to 2 decimal pleces.) Test statistic (e) At the 1 percent level of significance (a O1) does the sample exceed the manufacturer's claim? No O Yes (d) Find the pvalue. (Round intermediate calculations to 2 decimal places. Round your answer to 4 decimal pleces.) Pvalue

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