If a sample size is greater than 30, which of the following characteristics of the distribution of sample means is true?a.)The distribution of sample means has a binomial distribution.b.)The distribution of sample means is approximately normal.c.)Nothing can be assumed about the distribution of sample means.d.)The sample size needs to be increased by 10% so we can apply the Central Limit Theorem.

A researcher takes a simple random sample of 50 recent Science graduates in full-time employment and calculates their mean salary. Which of the following is a true statement about distribution of the sample mean?Select one:a.The Central Limit Theorem tells us it is normal.b.It may not be normal because the sample size is large.c.It may not be normal because we don't know that the population is normal.d.It will not be normal because the sample size is small.

Central Limit Theorem for sampling distribution is valid only when:Select one:a. Large samples drawn from any independent and identically distributed populationb. The population follows normal distributionc. Samples are drawn from any independent and identically distributed populationd. The population follows a normal distribution and the sample size should be at least 30

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.

The central limit theorem states that if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean:Group of answer choicesis approximately normal if n ≥ 30.is approximately normal if the underlying population is normal.has the same variance as the population.is approximately normal if n < 30.

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)