Ans: yes, and the calculated probability would be exact.
Since the sample of of normal distribution also follows normal distribution. Here mean ~N(50, 5/√60). So we can calculate the probability that sample mean lies between 45 and 60.
Question 2 (0.5 points) A random variable X follows a normal distribution with mean of 50...
Question 1 (0.5 points) A random variable X follows a normal distribution with mean of 50 and standard deviation of 5. Suppose we take a simple random sample of size 6 from the population above. Can we calculate the probability that the sample mean is between 45 and 60? (You do not need to actually calculate the probability for this question.) Yes, and the calculated probability would be exact. Yes, and the calculated probability would be approximate. No. Question 2...
Question 3 (0.5 points) A random variable X has a left-skewed distribution with mean of 50 and standard deviation of 5. Suppose we take a simple random sample of size 6 from the population above. Can we calculate the probability that the sample mean is between 45 and 60? (You do not need to actually calculate the probability for this question.) Yes, and the calculated probability would be exact. Yes, and the calculated probability would be approximate. No.
Page 1 Question 1 Suppose we take repeated random samples of size 20 from a population with a Select all that apply. mean of 60 and a standard deviation of 8. Which of the following statements is 10 points true about the sampling distribution of the sample mean (x)? Check all that apply. A. The distribution is normal regardless of the shape of the population distribution, because the sample size is large enough. B. The distribution will be normal as...
Suppose that a random variable X follows a distribution with mean 100 and variance 81. We take a random sample of 240 observations and calculate x. What is the probability that we calculate a sample mean larger than 101?
1. Given the probability distribution shown for an infinite population with the discrete random variable, x: X: 0 1 2 3 P(X) .2 .05 .3 .45 a. Determine the mean and standard deviation of x. b. For the sample size, n=2, determine the mean for each possible simple random sample from this population. c. For each simple random sample identified in part b, what is the probability that this particular sample will be selected? d. Combining the results of parts...
QUESTION 1 A random variable X follows a normal distribution with mean 350 and standard deviation 65. If a sample of size 15 is taken, find P(X> 325). (3 decimal places)
5. Suppose X follows a normal distribution with mean u = 200 and standard deviation o = 40. Find each of the following probabilities. (8 points) a. P(160 < x < 232) b. P(X > 160) C. P(X < 100) d. P(230 < x < 284) 6. Sup Suppose we know that SAT scores have a population average u = 1080 and a standard deviation o = 200. A university wants to give merit scholarships to all students with an...
The random variable X represents the roll of a 10-sided fair die. That is to say its sample space is the set {1,2,3,4,5,6,7,8,9,10}, with each outcome equally likely. Calculate the following population parameters: a.) The population mean: μx = _______ b.) The population variance and standard deviation: c.) The expected value E[X²] 9.) For the normal random variable X with mean μ = 50 and standard deviation σ = 4, a.) Find the probability P(x > 60) = b.) Find the probability (49 < x̄ <...
A population has a normal distribution with a mean of 50 and a standard deviation of 10. If a random sample of size 9 is taken from the population, then what is the probability that this sample mean will be between 48 and 54?
A population distribution has mean 50 and standard deviation 20. For a random sample of size 100, the sampling distribution of the sample mean has: A. mean 5 and standard deviation 2 B. mean 0.5 and standard deviation 0.2 C. mean 50 and standard deviation 0.2 D. mean 50 and standard deviation 2 E. mean 50 and standard deviation 20