Question

In: Statistics and Probability

Suppose samples of size 100 are drawn randomly from a population of size 1000 and the...

Suppose samples of size 100 are drawn randomly from a population of size 1000 and the population has a mean of 20 and a standard deviation of 5. What is the probability of observing a sample mean equal to or greater than 21?

Expert Solution

Solution:

Given that,

= 20

= 5

n = 100

So,

= 20

= ( / $\sqrt$ n) = (5/ $\sqrt$ 100 ) = 0.5

p ( 21 )

= 1 - p ( 21 )

= 1 - p ( - / ) ? ( 21- 20 / 0.5)

= 1 - p ( z ? 1 /0.5)

= 1 - p ( z ? 2)

Using z table

= 1 - 0.9772

= 0.0228

Probability = 0.0228

orchestra answered 3 years ago

a) If random samples of size 12 are drawn from a population with mean 7 and...

a) If random samples of size 12 are drawn from a population with mean 7 and standard deviation 2 , find the standard error of the distribution of sample means. b) Assume the sample is a random sample from a distribution that is reasonably normally distributed and we are doing inference for a sample mean. Find endpoints of a t-distribution with 0.025 beyond them in each tail if the sample has size n=26. c) Assume the sample is a random...

A random sample with replacement of size 100 is drawn from a population with mean 3.5...

A random sample with replacement of size 100 is drawn from a population with mean 3.5 and standard deviation 3. Use the normal approximation to calculate the probability that the sample average is between 3 and 4. Round your answer to three decimal places.

Consider a sample of size 100 drawn from a population that obeys an unknown distribution. It...

Consider a sample of size 100 drawn from a population that obeys an unknown distribution. It is known that the population-variance (of some quality characteristic) is 6. Let µ denote the population-mean. Consider the following test of a hypothesis about µ. H0 : µ = 70 H1 : µ ≠ 70 (a) Calculate Z0.005. Explain the meaning of Z0.005. (b) If the sample mean is observed to be 71, would you reject H0 with 99% confidence? What is the p-value...

Suppose that a sample of size 3 is drawn from a population consisting of the six...

Suppose that a sample of size 3 is drawn from a population consisting of the six values 4, 8, 5, 3, 8, and 4, and that the proportion of values that are greater than 4 is recorded. Find the sampling distribution of this statistic by listing all possible such samples of size 3. Find the mean and variance of the sampling distribution.

Suppose a random sample of size 40 was drawn from a normally distributed population, with a...

Suppose a random sample of size 40 was drawn from a normally distributed population, with a known population standard deviation of σ=6.4. a) What is the margin of error for a 95% confidence level? Round your response to at least 3 decimal places. b) What is the margin of error for a 90% confidence level? Round your response to at least 3 decimal places.

Suppose a simple random sample of size n=1000 is obtained from a population whose size is...

Suppose a simple random sample of size n=1000 is obtained from a population whose size is N=2,000,000 and whose population proportion with a specified characteristic is p = 0.22 a. What is the probability of obtaining x=250 or more individuals with the characteristic?

Suppose a simple random sample of size n= 1000 is obtained from a population whose size...

Suppose a simple random sample of size n= 1000 is obtained from a population whose size is N=2,000,000 and whose population proportion with a specified characteristic is p= 0.65. (a) Describe the sampling distribution of (b) What is the probability of obtaining x= 690 or more individuals with the characteristic? (c) What is the probability of obtaining x = 620 or fewer individuals with the characteristic?

A sample size of n=100 is drawn from a population whose standard deviation is =3.8 Find...

A sample size of n=100 is drawn from a population whose standard deviation is =3.8 Find the margin of error for a 95% confidence level.

Suppose a simple random sample of size n equals=1000 is obtained from a population whose size...

Suppose a simple random sample of size n equals=1000 is obtained from a population whose size is N equals=1,000,000 and whose population proportion with a specified characteristic is p=0.74. (b) What is the probability of obtaining x=770 or more individuals with the characteristic? (c) What is the probability of obtaining x=720 or fewer individuals with the characteristic? (Round to four decimal places as needed.) How to solve these problems in Statcrunch? Thank you!

Suppose that 100 items are drawn from a population f manufactured products and the weight, X,...

Suppose that 100 items are drawn from a population f manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a right skewed probability distibution with mean=150 oz and standard deviation=30 oz. Find the value of X-bar for which P(X-bar > ?) = 0.75.