Suppose x has a distribution with a mean of 70 and a standard deviation of 52. Random samples of size n = 64 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has a normal distribution with mean μx = 70 and standard deviation σx = 52. (b) Find the z value corresponding to x = 83. z = (83 - 70) / 52 = 0.25. (c) Find P(x < 83). (Round your answer to four decimal places.) P(x < 83) = P(z < 0.25) = 0.5987. (d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 83? Explain. No, it would not be unusual because more than 5% of all such samples have means less than 83.
Added by Ashley T.
Step 1
** Show more…
Show all steps
Close
Your feedback will help us improve your experience
Adi S and 85 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Suppose x has a distribution with a mean of 70 and a standard deviation of 12. Random samples of size n = 64 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has a normal distribution with mean μx = 70 and standard deviation σx = 12. (b) Find the z value corresponding to x = 73. z = (73 - 70) / 12 = 0.25 (c) Find P(x < 73). (Round your answer to four decimal places.) P(x < 73) = 0.5987 (d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 73? Explain. No, it would not be unusual because less than 5% of all such samples have means less than 73.
Adi S.
Suppose x has a distribution with a mean of 80 and a standard deviation of 20. Random samples of size n = 64 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has distribution with mean μx = and standard deviation σx = . (b) Find the z value corresponding to x = 75. z = (c) Find P(x < 75). (Round your answer to four decimal places.) P(x < 75) = (d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 75? Explain. Yes, it would be unusual because more than 5% of all such samples have means less than 75. No, it would not be unusual because less than 5% of all such samples have means less than 75. No, it would not be unusual because more than 5% of all such samples have means less than 75. Yes, it would be unusual because less than 5% of all such samples have means less than 75.
Lucas F.
A simple random sample of size n = 49 is obtained from a population that is skewed right with μ = 84 and σ = 7. (a) Describe the sampling distribution of x̄. (b) What is P(x̄ > 86)? (c) What is P(x̄ ≤ 81.85)? (d) What is P(82.95 < x̄ < 86.05)? (a) Choose the correct description of the shape of the sampling distribution of x̄. A. The distribution is skewed right. B. The distribution is approximately normal. C. The distribution is uniform. D. The distribution is skewed left. E. The shape of the distribution is unknown. Find the mean and standard deviation of the sampling distribution of x̄. μ_x̄ = σ_x̄ = (Type integers or decimals. Do not round.) (b) P(x̄ > 86) = (Round to four decimal places as needed.) (c) P(x̄ ≤ 81.85) = (Round to four decimal places as needed.) (d) P(82.95 < x̄ < 86.05) = (Round to four decimal places as needed.)
Shaiju T.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD