Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 48 minutes and standard deviation 18 minutes. A researcher observed 41 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N 48 b. What is the distribution of ? - N 48 c. What is the distribution of ? - N X- 18 d. If one randomly selected student is timed, find the probability that this student's time will be between 46 and 49 minutes. e. For the 41 students, find the probability that their average time studying is between 46 and 49 minutes. f. Find the probability that the randomly selected 41 students will have a total study time more than 1804 minutes. g. For part e) and f), is the assumption of normal necessary? O No Yes h. The top 15% of the total study time for groups of 41 students will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker? minutes Submit Question

The average final exam score for the statistics course is 82%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is different. The final exam scores for the 14 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 90, 78, 82, 59, 67, 71, 64, 78, 67, 57, 79, 86, 66, 56 What can be concluded at the the αα = 0.05 level of significance level of significance?  For this study, we should use    (t-test for a population mean,  z-test for a population proportion) The null and alternative hypotheses would be:       H0: (symbol) (symbol) ____              H1: (symbol) (symbol) ____               The test statistic (?,t,z) = ____  (please show your answer to 3 decimal places.) The p-value =  (Please show your answer to 4 decimal places.) The p-value is (symbol)  αα Based on this, we should  (accept, reject, fail to reject) the null hypothesis.…

Suppose that speed at which cars go on the freeway is normally with 71 mph and standard deviation 8 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places were possible.

The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 64 minutes and a standard deviation of 14 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected person at the hot springs stays longer then 57 minutes. c. The park service is considering offering a discount for the 7% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes. d. Find the Inter Quartile Range (IQR) for time spent at the hot springs. Q1: minutes Q3: minutes IQR: minutes