Suppose you have two normal distributions: one has μ = 16 and σ = 2 and the other has μ = 20 and σ = 3. Which of the following statements are true? Select all that apply.

Which of the following about the normal distribution is NOT true?

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

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

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)

Let X be normally distributed with mean μ and standard deviation σ > 0. Which of the following is false about the z value corresponding to a given x value?Multiple ChoiceA positive z = (x − μ)/σ indicates how many standard deviations x is above μ.The z value corresponding to x = μ is zero.The z value corresponding to a given value of x assumes any value between 0 and 1.A negative z = (x − μ)/σ indicates how many standard deviations x is below μ.