5.  Suppose the random variable X𝑋 is normally distributed with μ=18𝜇=18 and σ2=64𝜎2=64 . If the sample size is equal to 20, what is the sampling distribution of the sample mean, X¯𝑋¯ ?Multiple choice 3 Question 3  N(20,1.79)𝑁(20,1.79)   N(18,3.2)𝑁(18,3.2)   N(18,1.79)𝑁(18,1.79)   N(18,64)𝑁(18,64)

6.  Suppose the random variable X𝑋 is normally distributed with μ=40𝜇=40 and σ2=40𝜎2=40 . What is P(X¯≤42)P(𝑋¯≤42) if the sample size n𝑛 is equal to 10?Multiple choice 4 Question 3  0.6915  0.1587  0.8413  0.3085

Suppose we take repeated random samples of size 20 from a population with a mean of 60 and a standard deviation of 8. Which of the following statements is true about the sampling distribution of the sample mean (x̄)? Check all that apply. The distribution is normal regardless of the shape of the population distribution, because the sample size is large enough. The distribution will be normal as long as the population distribution is normal. The distribution's mean is the same as the population mean 60. The distribution's standard deviation is larger than the population standard deviation of 8.

4.  Suppose the random variable X𝑋 is normally distributed with μ=50𝜇=50 and σ2=16𝜎2=16 . What is P(49≤X≤55)P(49≤𝑋≤55) ?Multiple choice 2 Question 3  0.3756  0.4931  0.6734  0.2098

A normal population has mean μ =33 and standard deviation σ =7.(a) What proportion of the population is between 18 and 29?(b) What is the probability that a randomly chosen value will be between 26 and 36?

Sampling Distributions Checkpoint 2Question 1Select all that apply.10 pointsWhich of the following statements about the sampling distribution of the sample mean, x-bar, is true? Check all that apply. The distribution is normal regardless of the shape of the population distribution, as long as the sample size, n, is large enough. The distribution is normal regardless of the sample size, as long as the population distribution is normal. The distribution's mean is the same as the population mean. The distribution's standard deviation is smaller than the population standard deviation.Question 2Select one answer.10 pointsPictured below (in scrambled order) are three histograms. One of them represents a population distribution. The other two are sampling distributions of x-bar: one for sample size n = 5 and one for sample size n = 40.Based on the histograms, what is the most likely value of the population mean? 290 1 8 5Question 3Select one answer.10 pointsSuppose that a candy company makes a candy bar whose weight is supposed to be 50 grams, but in fact, the weight varies from bar to bar according to a normal distribution with mean μ = 50 grams and standard deviation σ = 2 grams.If the company sells the candy bars in packs of 4 bars, what can we say about the likelihood that the average weight of the bars in a randomly selected pack is 4 or more grams lighter than advertised? There is no way to evaluate this likelihood, since the sample size (n = 4) is too small. There is about a 16% chance of this occurring. There is about a 2.5% chance of this occurring. It is extremely unlikely for this to occur; the probability is very close to 0. There is about a 5% chance of this occurring.Question 4Select one answer.10 pointsWhen the population is not normally distributed, the sampling distribution of the mean approximates which of the following? A distribution that is not normal A slight positive skew A normal distribution given a large enough sample A normal distribution