What is the value of t*, the critical value of the t distribution for a sample of size 6, such that the probability of being greater than t* or less than -t* is 1%? t* =
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A: Mean(μ)=31standard deviation(σ)=5
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- A company that sells binders decides to run a promotion on their 1-inch and 2-inch size binders. Theydiscount the 1-inch binders to $1 per binder and discount the 2-inch binders to $2 per binder. They limitsales to a quantity of 5 of each size of binder per customer. The probability distribution of “X = the numberof 1-inch binders purchased by a single customer during the promotion period” is given in the table below. X 1 2 3 4 5 P(X) 0.02 0.09 0.12 0.15 0.62 a) Compute the mean and standard deviation of X. b) The company’s cost of manufacturing a single 1-inch binder is $0.25. What is the expected profit (indollars) that the company will make, per customer, for 1-inch binder sales during the promotion? c) The mean and standard deviation of “Y = the number of 2-inch binders purchased by a singlecustomer” is 2.74 and 1.25, respectively. Assume that the number of 1-inch and 2-inch binderspurchased are independent random variables. What are the mean and standard deviation of the…Suppose that a random sample of size 25 is to be selected from a population with mean 46 and standard deviation 8. What is the approximate probability that X will be more than .5 away from the population mean?What is the value of t*, the critical value of the t distribution for a sample of size 22, such that the probability of being greater than t* or less than -t* is 1%? t* = 7.3
- 3. If Z is a random variable having the standard normal distribution, find i. P(Z - 1.08) iii. P(-1.90Suppose data x is distributed with poisson distribution with λ=100 then find the probability of x=99A random sample of n= 4 is obtained from a normal distribution μ=30, σ=8. What is the probability the sample mean will be smaller than M = 22? Report to the thousandthsThe manager of a baseball team has determined the number of walks, x, issued in a game by one of the pitchers. The probability distribution for x is as follows: P(x) 1/20 X 1 2/20 2 3/20 3 11/20 4 3/20 a) Is this a correct probability distribution? Why or why not? b) Calculate the mean (expected value) for x. c) Construct the probability distribution histogram for the number of 'walks'.X is uniformly distributed between 14 and 23. What is the Expected value of X?Suppose that you take a sample of size 40 from a population that is normally distributed. Can the sampling distribution of x̄ be approximated by a normal probability distribution? What if the population was not normally distributed, can the sampling distribution of x̄ be approximated by a normal probability distribution?Use the normal approximation to the binomial to calculate the probability of getting more than 39 defectives in a random sample of 400 taken from a population which is 8% defective.What is the probability of obtaining a z score that is as extreme as or more extreme than 1.96?Suppose weights, in pounds, of dogs in a city have an unknown distribution with mean 31 and standard deviation 5 pounds. A sample of size n=39 is randomly taken from the population and the sum is taken. What is the probability that the resulting sum is between 1180 and 1194 pounds?