Bolts produced by a machine have a mean weight of 50gm and a standard deviation of 2gm. If 300 random samples of size 36 are drawn from this population, determine the expected mean and standard deviation of the sampling distribution of means.a.mean = 50gm, sd = 0.33gmb.mean = 50gm, sd = 2gmc.mean = 8.33gm, sd = 0.33gmd.mean = 8.33gm, sd = 2gm
Question
Bolts produced by a machine have a mean weight of 50gm and a standard deviation of 2gm. If 300 random samples of size 36 are drawn from this population, determine the expected mean and standard deviation of the sampling distribution of means.a.mean = 50gm, sd = 0.33gmb.mean = 50gm, sd = 2gmc.mean = 8.33gm, sd = 0.33gmd.mean = 8.33gm, sd = 2gm
Solution
The expected mean of the sampling distribution of means is equal to the mean of the population. So, the mean will be 50gm.
The standard deviation of the sampling distribution of means (also known as the standard error) is equal to the standard deviation of the population divided by the square root of the sample size. So, the standard deviation will be 2gm / sqrt(36) = 0.33gm.
So, the correct answer is a. mean = 50gm, sd = 0.33gm.
Similar Questions
A population of adult free-range turkeys has a mean weight of 8.5 kg and a standard deviation of 1.2 kg. A random sample of size 10 is taken from this population. Find the mean and the standard deviation for the total weight of this sample of size 10.
In a distribution exactly normal with mean 47.5 Kilogram, 89.97% of the items are under 70 kilogram weight. Then which of the following is the standard deviation of the distribution? Given that area under standard normal curve from Z=0 to Z=1.28 is 0.3997.
A machine designed to cut steel tubing into 2.4 metre lengths produces pipes with lengths that arenormally distributed with a mean 2.4 metres and standard deviation 0.03 metres.A random sample of 9 pipe lengths is measured. Which of the following is the most accurate description of the distribution of the sample mean length?Question 2Select one:a.It has a mean of 2.4 metres and a standard error of 0.01 metres.b.It is normal with a mean of 2.4 metres and a standard error of 0.03 metres.c.It is normal with a mean of 2.4 metres and a standard error of 0.01 metres.d.It has a mean of 2.4 metres and a standard error of 0.03 metres.
The mean weight of 1000 students at a certain college is 62 kg, and the standard deviation is 5kg. Assuming that the weights are normally distributed, find the probability that a randomly selected student weighs between 55 and 60kg.a.0.3446b.0.0808c.0.2638d.0.7362
29.The standard deviation of the sample means is equal to which of the following? A. population standard deviation divided by the square root of n (sample size) B. sample standard deviation divided by n (sample size) C. sample standard deviation divided by the square root of n (sample size) D. population standard deviation divided by n (sample size)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.