Suppose 44% of politicians are lawyers. If a random sample of size 411 is selected, what...

Suppose 44% of politicians are lawyers.

If a random sample of size 411 is selected, what is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 7%? Round your answer to four decimal places.

Solutions

Expert Solution

Solution

Given that,

p = 0.44

1 - p = 1 - 0.44 = 0.56

n = 411

= p = 0.44

= $\sqrt$ p ( 1 - p ) / n

= $\sqrt$ (0.44 * 0.56) / 411 = 0.0245

= 0.0245

P(0.37 < < 0.51) = P( (0.37 - 0.44) / 0.0245 < ( - ) / < (0.51 - 0.44) / 0.0245)

= P(-2.86 < z < 2.86)

= P(z < 2.86) - P(z < -2.86)

= 0.9979 - 0.0021

= 0.9958

Probability = 0.9958

orchestra answered 2 years ago

Next > < Previous

Related Solutions

Suppose 59% of politicians are lawyers. If a random sample of size 750 is selected, what...

Suppose 59% of politicians are lawyers. If a random sample of size 750 is selected, what is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 5%? Round your answer to four decimal places.

Suppose that a random sample of size 64 is to be selected from a population with...

Suppose that a random sample of size 64 is to be selected from a population with mean 40 and standard deviation 5. (a) What are the mean and standard deviation of the x sampling distribution? μx = 1 40 Correct: Your answer is correct. σx = 2 .625 Correct: Your answer is correct. (b) What is the approximate probability that x will be within 0.2 of the population mean μ? (Round your answer to four decimal places.) P = 3...

Suppose that a random sample of size 64 is to be selected from apopulation with...

Suppose that a random sample of size 64 is to be selected from a population with mean 50 and standard deviation 7. (Use a table or technology.)(a)What are the mean and standard deviation of thexsampling distribution?μxσx=(b)What is the approximate probability thatxwill be within 0.5 of the population mean μ? (Round your answer to four decimal places.)(c)What is the approximate probability that x will differ from μ by more than 0.8? (Round your answer to four decimal places.)

Suppose that a random sample of size 64 is to be selected from a population with...

Suppose that a random sample of size 64 is to be selected from a population with mean 40 and standard deviation 5. a) What is the approximate probability that x will differ from μ by more than 0.8? (Round your answer to four decimal places.)

1. Suppose that a random sample of size 64 is to be selected from a population...

1. Suppose that a random sample of size 64 is to be selected from a population with mean 40 and standard deviation 5. a. What is the mean of the ¯xx¯ sampling distribution? b. What is the standard deviation of the ¯xx¯ sampling distribution? c. What is the approximate probability that ¯xx¯ will be within 0.5 of the population mean μμ? d. What is the approximate probability that ¯xx¯ will differ from μμ by more than 0.7? 2. A Food...

Suppose a random sample of size 53 is selected from a population with σ = 9....

Suppose a random sample of size 53 is selected from a population with σ = 9. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate). a. The population size is infinite (to 2 decimals). b. The population size is N = 50,000 (to 2 decimals). c. The population size is N = 5000 (to 2 decimals). d. The population size is N = 500 (to...

Suppose a random sample of size 50 is selected from a population with σ = 8....

Suppose a random sample of size 50 is selected from a population with σ = 8. Find the value of the standard error of the mean in each of the following cases. (Use the finite population correction factor if appropriate. Round your answers to two decimal places.) (a) The population size is infinite. (b) The population size is N = 50,000. (c) The population size is N = 5,000. (d) The population size is N = 500.

Suppose a random sample of size 51 is selected from a population with = 12. Find...

Suppose a random sample of size 51 is selected from a population with = 12. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate). a. The population size is infinite (to 2 decimals). b.The population size is N = 50,000 (to 2 decimals). c. The population size is N = 5,000 (to 2 decimals). d.The population size is N = 500 (to 2 decimals).

Suppose a random sample of size 60 is selected from a population with = 8. Find...

Suppose a random sample of size 60 is selected from a population with = 8. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate). The population size is infinite (to 2 decimals). The population size is N = 50,000 (to 2 decimals). The population size is N = 5,000 (to 2 decimals). The population size is N = 500 (to 2 decimals).

Suppose a random sample of size 56 is selected from a population with = 8. Find the...

Suppose a random sample of size 56 is selected from a population with = 8. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate). The population size is infinite (to 2 decimals). The population size is N = 50,000 (to 2 decimals). The population size is N = 5,000 (to 2 decimals). The population size is N = 500 (to 2 decimals).

Subjects