Question

In: Statistics and Probability

a simple random sample of size 36 is taken from a normal population with mean 20...

a simple random sample of size 36 is taken from a normal population with mean 20 and standard deivation of 15. What is the probability the sample,mean,xbar based on these 36 observations will be within 4 units of the population mean. round to the hundreths place

Expert Solution

Solution :

Given that,

mean = = 20

standard deviation = = 15

n = 36

= = 20

= / n = 15 / 36 = 2.5

P(16 < < 24)

= P[(16 - 20) / 2.5 < ( - ) / < (24 - 20) / 2.5)]

= P(-1.60 < Z < 1.60 )

= P(Z < 1.60) - P(Z < -1.60)

Using z table,

= 0.95 - 0.05

= 0.90

orchestra answered 3 years ago

A random sample of size 36 is taken from a population having mean 20 and variance...

A random sample of size 36 is taken from a population having mean 20 and variance 9.What is the probability that the sample meanXwill be at least 21?

A simple random sample of size n=36 is obtained from a population with mean=89 and standard...

A simple random sample of size n=36 is obtained from a population with mean=89 and standard deviation = 6 (c) What is P ( x overbar less than or equal to 86.65)? (d) What is P(88.5 < x overbar < 91.25)? (a) Describe the sampling distribution of x overbar. (b) What is P ( x overbar > 90.85 )?

Random sample of size n=19 is taken from a Normal population, sample mean is 11.5895, standard...

Random sample of size n=19 is taken from a Normal population, sample mean is 11.5895, standard deviation is 1.0883. 1. At the 2% level, test whether it is reasonable to believe that the true population variance is larger than 1. Using the scenario from above, do the following 2. Derive the power function. Show your work. 3. Using R, graph the power function for 0.5 < sigma^2 < 3.5. 4. Pretend that the sample size was actually 56. Plot this...

A random sample of size 15 is taken from a population assumed to be normal, with...

A random sample of size 15 is taken from a population assumed to be normal, with sample mean = 1.2 and sample variance = 0.6. Calculate a 95 percent confidence interval for population mean.

In a simple random sample of size 50, taken from a population, 23 of the individuals...

In a simple random sample of size 50, taken from a population, 23 of the individuals met a specified criteria. a) What is the margin of error for a 90% confidence interval for p, the population proportion? Round your response to at least 3 decimal places. b) What is the margin of error for a 95% confidence interval for p? Round your response to at least 3 decimal places.

A simple random sample of size n=36 is obtained from a population that is skewed right...

A simple random sample of size n=36 is obtained from a population that is skewed right with μ=74 and σ=24. (a) Describe the sampling distribution of overbarx. (b) What is P ( x overbar > 80.6 )? (c) What is P (x overbar ≤64.6)? (d) What is P ( 70<x<80?) (a) Choose the correct description of the shape of the sampling distribution of overbarx. A.The distribution is skewed left. B.The distribution is uniform. C.The distribution is approximately normal. D.The distribution...

a. A random sample of 25 is taken from a normal distribution with population mean =...

a. A random sample of 25 is taken from a normal distribution with population mean = 62, and population standard deviation = 7. What is the margin of error for a 90% confidence interval? b. Repeat the last problem if the standard deviation is unknown, given that the sample standard deviation is S=5.4

Consider a sample of size 22 taken from a normal population. The sample mean is 2.777...

Consider a sample of size 22 taken from a normal population. The sample mean is 2.777 and the sample standard deviation is 0.13. We test Ho: μ = 2.7 versus H1: μ > 2.7 at the α = 0.05 level. The rejection region and our decision are Select one: a. t > 1.721; REJECT Ho b. t > 2.080; REJECT Ho c. t > 2.074; REJECT Ho d. t > 1.717; REJECT Ho

A simple random sample of size n =20 is drawn from a population that is normally...

A simple random sample of size n =20 is drawn from a population that is normally distributed. The sample mean is found to be x = 61 and the sample standard deviation is found to be s =12 Construct a 95% confidence interval about the population mean.

A simple random sample of size n=40 is drawn from a population. The sample mean is...

A simple random sample of size n=40 is drawn from a population. The sample mean is found to be x=121.7 and the sample standard deviation is found to be s=13.3. Construct a 99% confidence interval for the population mean. The lower bound is (Round to two decimal places as needed.)