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- The standard deviation of the scores on a skill evaluation test is 363 points with a mean of 1239 points. If 335 tests are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 23 points? Round your answer to four decimal places.Suppose the amount of change IWU students carry is exponentially distributed with a mean of $0.88. Suppose that we randomly pick 25 IWU students and learn how much change they have. What type of distribution does the population, which is the change carried by IWU students, follow? What are the mean and standard deviation of the population? (6 points) What type of distribution does the sample mean follow? What are the mean and standard deviation of the sample mean? (6 points) Find the probability that the average change of 25 IWU students was between $0.80 and $1.00. Graph the situation, shade in the area to be determined, and find the probability. (6 points)As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution
- As the sample size increases, the variance of the sample mean Select one: a. increases b. not enough info to know c. decreases d. stays constantSuppose a batch of steel rods produced at a steel plant have a mean length of 150 millimeters, and a variance of 100. If 275 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by greater than 0.57 millimeters? Round your answer to four decimal places.Suppose we use the mean of a random sample of size n = 100 to estimate the mean of a population with σ = 30 . Use the central limit theorem to compute the probability that the error is less than 6. Express your answer as a decimal using 4 decimal places. Give the exact value on the chart. Do not round your answer.....
- Consider the mean cost of getting a four-year college degree. The middle interval which captures 95% of mean costs from samples of n = 75 graduates is (x̅₁, x̅₂) = $60,142 $68,446 25 What is the population mean cost of getting a college degree? a $62,384 b $63,014 c $63,651 d $64,294A __________ is a characteristic of a population. Multiple Choice normal distribution descriptive statistics parameter sampleSuppose you select a random sample of 16 students from a population that has mean of µ = 75 and standard deviation of ơ = 20. You want to know what would be considered a ‘typical’ sample mean for a sample of n = 16. To answer your question, you compute the two sample means that define the middle 95% of the distribution of sample means. Show your work, sketch the distribution, and shade in the area of interest. Hint: Sample means that are in the extreme 5% of the distribution (2.5% in each tail of the distribution) are considered ‘atypical’ or ‘extreme.’
- You collected a sample from a population which you realized has very high standarddeviation. You want to estimate the population parameter from this sample. You thinkthat your interval will be very wide, what you can do to narrow it down without changingyour confidence level. Will your suggestion to improve the width of the interval increasethe probability of the true mean lying in that interval?A lumber company is making boards that are 2701.02701.0 millimeters tall. If the boards are too long they must be trimmed, and if they are too short they cannot be used. A sample of 2222 boards is made, and it is found that they have a mean of 2703.92703.9 millimeters with a variance of 100.00100.00. Is there evidence at the 0.10.1 level that the boards are either too long or too short? Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the boards are either too long or too short?Of 900 people treated with a new drug, 180 show allergic reaction. Construct a 98% confidence interval for the true proportion of the population who would show an allergic reaction.