What is the value of t*, the critical value of the t distribution for a sample of size 26, such that the probability of being greater than t* is 1%? t* =
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What is the value of t*, the critical value of the t distribution for a
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- 3. Let Y,,. , Y, be a random sample from a normal distribution with mean 30 and standard deviation 3. What is the probability the largest observation is greater than 30?You want to find the probability that people will return a shopping cart to the corral after loading the groceries in their vehicle. For a 4 hours period, you observe the number of people who returned their cart and the number who did not. A success in this case would be that the person returned their cart. Choose the best statistical tool to calculate this probability A. Use the Central Limit Theorem to find the probability that the sample mean exceeds a certain value B. Use the empirical rule to find the number of cars that bracket 68% of the data C. Calculate a confidence interval for the population mean D. Calculate the total number of successes divided by the total number of observations to find the observed probabilityWhat 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
- 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)?Suppose that 70% of Americans support the death penalty for persons convicted of murder. Let p> (p hat) be the sample proportion of proportion of people who support the death penalty in an SRS of Americans. Suppose we set our sample size to be n=84. What is the probability of choosing an SRS in which between 65% and 73% of the people in the people in the sample support the death penalty? That is, find P(0.65<p(phat)<0.73). Show your work and box your answer.The annual rainfall (in inches) in a certain region is normally distributed with mean = 40 and o=4. What is the probability that starting with this year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? What assumption are you making?
- 1. Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 10.0 minutes and standard deviation of 4.0 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 41, customers in the first line and m₂ = 51 customers in the second line. Find the probability that the difference between the mean service time for the shorter line and the mean service time for the longer X₂ one ¹2 is more than 0.4 minutes. Assume that the service times for each customer can be regarded as independent random variables.What is the probability of scoring above a z-score of -0.08?5. What is the value of t, the critical value of the distribution with 8 degrees of freedom, which satisfies the condition that the probability is 0.10 of being larger than tᵒ? (a) 1.415 (b) 1.397 (c) 1.645 (d) 2.896 (e) 0.906.
- A doctor is interested in the proportion of patients which live at least 5 years after being diagnosed with stage 4 breast cancer. He randomly selects 138 patients diagnosed with stage 4 breast cancer and follows them for 5 years. Suppose the true 5 year survival rate for stage 4 breast cancer is 38%. 1. How are the collection of all sample proportions of samples of size 138 distributed? NO 2. What is the probability that fewer than 34% of the patients studied survived for at least 5 years? o List the z-scores needed to calculate the result. If there is more than one z-score, separate the values with a comma. o There is a survived for at least 5 years. 3. What is the probability that more than 45% of the patients studied survived for at least 5 years? chance that fewer than 34% of the patients studied o List the z-scores needed to calculate the result. If there is more than one z-score, separate the values with a comma. O There is a survived for at least 5 years. chance that more than…Suppose the random variable Z follows a standard normal distribution,, Then thevalue of PIZ<-339) is O A 0.9997 O B. 0,0003 O C. 1.000 O D. 0.0000A sample of size 14 will be drawn from a population with mean 100 and standard deviation 40. Is it appropriate to use the normal distribution to find probabilities for x? Yes O No X
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