A binomial random variable has mean 5 and variance 4. Find the values of n and p that characterize the distribution of this random variable
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A binomial random variable has
and p that characterize the distribution of this random variable
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- Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 254 hybrid sedans and get a mean of 26 mpg with a standard deviation of 4 mpg. Also, 237 non-hybrid sedans get a mean of 24 mpg with a standard deviation of 6 mpg. Suppose that both populations are known to be normal distributed. Conduct a hypothesis test to evaluate the manufacturers' claim. Test at a 4% level of significance. Let population 1 denote non-hybrids and population 2 denote hybrids. (a) H0 : μ1 ______ μ2 (b) Ha : μ1 _______ μ2 (c) In words, state what your random variable represents.The random variable is the (mean / difference in the / difference in the mean) miles per gallon of non-hybrid sedans and hybrid sedans.A sum of the squared independent standard normal random variable follows what distribution.do fast
- Assume that the square footage of a residential house in the US is normally distributed with a mean=1000 and standard deviation=150 square feet. If we select a random house what is the probability that it will be at most 1050 square feet?The University of Florida is interested in determining if there is a difference in the amount of money spent on food every two weeks between male and female students. They take a random sample of 20 male students (group 2) and 20 female students (group 1). They also find that xbar2 is 106 with a standard deviation of 14, and xbar1 is 146 with a standard deviation of 39. Do not assume equal variances. Find the test statistic for the difference in the amount of money spent. (Round your answer to one number after the decimal.)IQs measured on a certain scale are normally distributed with a mean of 90 and a variance of 400. whats the probability that a random person will have an IQ between 120 and 130. the IQ of 51 people was taken, a sample mean of 90 and standard deviation of 64 was obtained. does this support that people tend to have IQs<100? use a 5% level of significance.
- A study of blood samples of 64 men shows a mean count of 5million RBC per cubic ml., with a variance of 0.06. A tabulation of64 women from the same population group show a mean countof 4.5 million, with a variance of 0.13. What is the probability offinding a woman with a count of less than 5 million?Suppose that the fraction of defective modems shipped by a data-communications vendor has an approximation beta distribution with a=5 and b=21. find the mean and variance of the fraction of defective modems per shipment What is the probability that a randomly selected shipment will contain at least 30 % defectives? What is the probability that a randomly selected shipment will contain no more than 5 % defectives?Explain how the special formulas for the mean and standard deviation of a binomial or Poisson random variable are derived.
- The life span of a certain wood cutting machine manufactured by a factory has a normal distribution with a guarantee that any machine that stars malfunctioning within 36 months of the purchase will be replaced by a new one. How many percentages of machines are expected to be replaced in the following cases? Mean of 60 months and variance of 64 months2 Mean of 45 months and variance of 36 months2 Mean of 75 months and variance of 16 months2The service times for customers coming through a checkout counter in a retail store are independentrandom variables with mean 1.5 minutes and the variance 1.0. Approximate the probability that 100customers can be served in less than (a) 2 hours (b) 3 hours of total service time.A researcher decides to measure anxiety in group of bullies and a group of bystanders using a 23-item, 3 point anxiety scale. Assume scores on the anxiety scales are normally distributed and the variance among the group of bullies and bystanders are the same. A group of 30 bullies scores an average of 21.5 with a sample standard deviation of 10 on the anxiety scale. A group of 27 bystanders scored an average of 25.8 with a sample standard deviation of 8 on the anxiety scale. You do not have any presupposed assumptions whether bullies or bystanders will be more anxious so you formulate the null and alternative hypothesis based on that.
