The number of bytes downloaded per second on an information channel has mean 105 and standard deviation 104. Among the factors influencing the rate is congestion, which produces alternating periods of faster and slower transmission. Let X represent the number of bytes downloaded in a randomly chosen five-second period. Is it reasonable to assume that μX = 5 × 105? Explain. Is it reasonable to assume that σX = √5 x 104 ? Explain.

researchers calculated for their study that the mean difference () = 5.65 and the SE of the Mean Difference () = 2.58, the t value is _____

Explain the Mean Value Theorem with a sketch.

A statistics professor for STAT 250 wants to investigate how long it takes students to complete Exam 1. The times that it took all 715 STAT 250 students in Spring 2022 were recorded in the data set “Time to Complete Exam 1” found in StatCrunch. The time is recorded in minutes. A student who completed the exam in 50:30 (50 minutes and 30 seconds) would be recorded as 50.5 minutes Column Mean Std. dev. Sample 26 (Time) 43.93 7.14 1) Does the mean calculated come from a sampling distribution that is approximately Normal? Check all three conditions of the Central Limit Theorem using one complete sentence for each condition to answer this question 2) Calculate the probability that, in a random sample of 26 students, the mean time to complete Exam 1 is 50 minutes or more. Complete this part by standardizing and using the Standard Normal Table to obtain this probability. Show all work and type all calculations.