Question

In: Statistics and Probability

A sample of n=25 scores is selected from a normal population with μ = 100 and...

A sample of n=25 scores is selected from a normal population with μ = 100 and σ = 20 .

a. What is the probability that the sample mean will be greater than 120?

b. What is the probability that the sample mean will be less than 105?

c. What is the p (90 < M < 110)?

Solutions

Expert Solution

z score for normal distribution formula

z = (M - μ) / (σ / sqrt(n))

a. What is the probability that the sample mean will be greater than 120?

z = (120 - 100) / (20/sqrt(25)) = 5

P(Z > 5) = 0

The probability that the sample mean will be greater than 120 = 0

b. What is the probability that the sample mean will be less than 105?

z = (105 - 100) / (20/sqrt(25)) =1

P(Z < 1) = 0.8413

c. What is the p (90 < M < 110)?

z = (90 - 100) / (20/sqrt(25)) = -3

z = (110 - 100) / (20/sqrt(25)) = 3

p (90 < M < 110) = 0.9973


Related Solutions

A random sample of n = 100 scores is selected from a normal population with a...
A random sample of n = 100 scores is selected from a normal population with a mean of μ = 60 and a standard deviation of σ = 20. What is the probability of obtaining a sample mean greater than M = 57?
A random sample of n =100 is selected from a normal population with mean μ =...
A random sample of n =100 is selected from a normal population with mean μ = 24 and standard deviation σ = 1.25. Find the probability that  is less than 24.3
A sample of n = 4 individuals is selected from a normal population with μ = 70 and σ = 10.
  3) A sample of n = 4 individuals is selected from a normal population with μ = 70 and σ = 10. A treatment is administered to the individuals in the sample, and after the treatment, the sample mean is found to be 75.      a) On the basis of the sample data, can you conclude that the treatment has a significant effect?           (Use a two-tailed test with α = .05).      b) Suppose that the sample consisted...
​If, in a sample of n=25 selected from a normal​ population, X=52 and S=10​, what is...
​If, in a sample of n=25 selected from a normal​ population, X=52 and S=10​, what is your statistical decision if the level of​ significance, a, is 0.05 the null​ hypothesis, H0​, is μ=50, and the alternative​ hypothesis, H1, is μ≠50?
The population of IQ scores form a normal distribution with a μ = 100 and a...
The population of IQ scores form a normal distribution with a μ = 100 and a standard deviation of σ = 10. What is the probability of obtaining a sample mean greater than M = 97, For a random sample of n = 9 For a random sample of n = 25 people
A random sample of n measurements was selected from a population with unknown mean μ and...
A random sample of n measurements was selected from a population with unknown mean μ and standard deviation σ=35 for each of the situations in parts a through d. Calculate a 95​% confidence interval for muμ for each of these situations. a. n=75​, x overbarx=22 b. n=150​,x overbarxequals=110 c. n=90​, x overbarxequals=18 d. n=90​,x overbarxequals=4.69 e. Is the assumption that the underlying population of measurements is normally distributed necessary to ensure the validity of the confidence intervals in parts a...
A random sample of n measurements was selected from a population with unknown mean μ and...
A random sample of n measurements was selected from a population with unknown mean μ and standard deviation σ = 15 for each of the situations in parts a through d. Calculate a 99% confidence interval for μ for each of these situations. a. n = 75, x̄ = 27 b. n = 150, x̄ = 105 c. n = 125, x̄ = 16 d. n = 125, x̄ = 5.37 e. Is the assumption that the underlying population of...
A sample of n = 9 scores is obtained from a normal population distribution with σ...
A sample of n = 9 scores is obtained from a normal population distribution with σ = 12. The sample mean is M = 60. a. With a two-tailed test and α = .05, use the sample data to test the hypothesis that the population mean is μ = 65. b. With a two-tailed test and α = .05, use the sample data to test the hypothesis that the population mean is μ = 55. c. In parts (a) and...
A researcher selects a sample of n=25 individuals from a population with a mean of μ=60...
A researcher selects a sample of n=25 individuals from a population with a mean of μ=60 and standard deviation of σ=10 and administers a treatment. The researcher predicts that the treatment will increase scores. Following the treatment, the average scores for this sample is M=65. 1. Using symbols, state the hypothesis for a one-tailed test. 2. Calculate the z-score and place this on a standardized normal distribution. 3. With a one-tail α=0.05, state the conclusion of these findings. 4. Calculate...
8. A sample of n = 4 individuals is selected from a normal population with m...
8. A sample of n = 4 individuals is selected from a normal population with m = 70 and s = 10. A treatment is administered to the individuals in the sample, and after the treatment, the sample mean is found to be M = 75. A. On the basis of the sample data, can you conclude that the treatment has a significant effect? Use a two-tailed test with a = .05. B. Suppose that the sample consisted of n...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT