A random sample of size n = 36 is obtain from a population with µ= 80,...

A random sample of size n = 36 is obtain from a population with µ= 80, and standard deviation =18.

(a). Describe the sampling distribution . (b). What is P(77 << 85 )?

Solutions

Expert Solution

Solution :

Given that ,

mean = = 80

standard deviation = = 18

n = 36

= 80

= / $\sqrt$ n= 18/ $\sqrt$ 36=3

P(77< <85 ) = P[(77 - 80) /3 < ( - ) / < (85 - 80) /3 )]

= P( -1< Z < 1.67)

= P(Z < 1.67) - P(Z < -1)

Using z table

=0.9525 - 0.1587

probability= 0.7938

orchestra answered 1 year ago

Next > < Previous

Related Solutions

5. A random sample of size n = 36 is obtain from a population with µ=...

5. A random sample of size n = 36 is obtain from a population with µ= 60 and standard deviation 12 (a). Describe the sampling distribution . (b). What is P(76.5 << 85.5 )?

A simple random sample of size n = 64 is obtained from a population with µ...

A simple random sample of size n = 64 is obtained from a population with µ = 112 and σ = 24. What is P(x ¯ ≤ 109.5)? (Give answer in decimal form and round answer to two 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 simple random sample of size n=49 is obtained from a population with µ=83 and σ=21....

A simple random sample of size n=49 is obtained from a population with µ=83 and σ=21. Describe the sampling distribution of x̄, is this distribution approximately normal. (enter Yes or No) What is P(x̄>88.1)=

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 )?

A random sample of size n = 100 is taken from a population of size N...

A random sample of size n = 100 is taken from a population of size N = 600 with a population proportion of p =0.46. Is it necessary to apply the finite population correction factor? Calculate the expected value and standard error of the sample proportion. What is the probability that the sample mean is less than .40?

A random sample of size n = 69 is taken from a population of size N...

A random sample of size n = 69 is taken from a population of size N = 971 with a population proportion p = 0.68. a-1. Is it necessary to apply the finite population correction factor? Yes or no? a-2. Calculate the expected value and the standard error of the sample proportion. (Round "expected value" to 2 decimal places and "standard error" to 4 decimal places.) Expected Value- Standard Error- b. What is the probability that the sample proportion is...

A random sample of size n = 71 is taken from a population of size N...

A random sample of size n = 71 is taken from a population of size N = 639 with a population proportion p = 0.73. a-1. Is it necessary to apply the finite population correction factor? a-2. Calculate the expected value and the standard error of the sample proportion. (Round "expected value" to 2 decimal places and "standard error" to 4 decimal places.) b. What is the probability that the sample proportion is less than 0.66? (Round “z” value to...

A random sample of size n = 152 is taken from a population of size N...

A random sample of size n = 152 is taken from a population of size N = 3,300 with mean μ = −71 and variance σ2 = 112. [You may find it useful to reference the z table.] a-1. Is it necessary to apply the finite population correction factor? Yes No a-2. Calculate the expected value and the standard error of the sample mean. (Negative values should be indicated by a minus sign. Round "standard error" to 2 decimal places.)...

A random sample of size n = 472 is taken from a population of size N...

A random sample of size n = 472 is taken from a population of size N = 9,700 with mean μ = −63 and variance σ2 = 176. [You may find it useful to reference the z table.] A-1 Is it necessary to apply the finite population correction factor? Yes No a-2. Calculate the expected value and the standard error of the sample mean. (Negative values should be indicated by a minus sign. Round "standard error" to 2 decimal places.)...

Subjects