Question

In: Statistics and Probability

A random variable, X, has a population mean, µ = 155, and a population standard deviation,...

A random variable, X, has a population mean, µ = 155, and a population standard deviation, σ = 10. What is the probability that X is more than 180?

Answer


PART II. A random variable, X, has a population mean, µ = 155, and a population standard deviation, σ = 10. To study the population, a random sample of 64 observations is collected and data is recorded. What is the probability that a sample mean will exceed 180?

Answer

Using PART II information, what is the probability that a sample mean will exceed 158?

Answer


In PART I, what assumption did you make about the random variable's distribution?

Answer

In PART II, what assumption did you make about the random variable's distribution?

Answer


Why? Answer

Solutions

Expert Solution

In part first distribution is normal ( 155,10)

In part second distribution is normal ( 155,10/√64) i.e. (155,10/8)=(155,1.25)

Because for sampling distribution standard deviation will be /√n

Please like ?

orchestra answered 1 year ago
Next > < Previous

Related Solutions

for a continuous random variable x, the population mean and the population standard deviation are 54...
for a continuous random variable x, the population mean and the population standard deviation are 54 and 12 respectively. you extract a sample of 36 elements from this population. the mean of the sampling distribution of the sample mean is:
Part A: Suppose a random variable X have mean of µ and standard deviation σ. Let...
Part A: Suppose a random variable X have mean of µ and standard deviation σ. Let a and b be constants. i) Derive the expected value of aX + b. ii) Derive standard deviation of aX + b Part B: Suppose that in country A, the price of certain good has a mean of $100 and a variance of 25, in A-dollars. Country B has a fixed exchange rate with A so that it takes 2 B-dollars to buy 1...
Given a random variable ? has population mean ? = 20 and standard deviation ? =...
Given a random variable ? has population mean ? = 20 and standard deviation ? = 5. a.) For the sampling distribution of the sample mean ?, for ? = 50 trials what are the mean and standard deviation? ??bar = _____________, ??bar =_____________. b.) What is the probability that the sample mean will be in the interval 19 < ?bar < 21 ? ?(19 < ? < 21) =_____________. (give answer to at least 4 signifiant figures.)
Suppose we know that a random variable X has a population mean µ = 400 with...
Suppose we know that a random variable X has a population mean µ = 400 with a standard deviation σ = 100. What are the following probabilities? (12 points) The probability that the sample mean is above 376 when n = 1600. The probability that the sample mean is above 376 when n = 400. The probability that the sample mean is above 376 when n = 100. The probability that the sample mean is above 376 when n =...
For normal population with known standard deviation, the x% confidence interval for the population mean µ...
For normal population with known standard deviation, the x% confidence interval for the population mean µ has a lower end point (z times the standard error) below the sample mean and a upper end point (z times the standard error) above the sample mean. That is, the x% CI is given as Sample mean ± z *standard error For 95% CI, the value for z is Answer 1Choose...2.581.6451.280.9751.96 For 80% CI, the value for z is Answer 2Choose...2.581.6451.280.9751.96 For 90%...
Let Z be a normal random variable with mean µ = 0 and standard deviation σ...
Let Z be a normal random variable with mean µ = 0 and standard deviation σ = 1, that is, Z ∼ N(0, 1). Find each of the following: (a) P(Z ≤ −1.13). (b) P(Z ≥ −2.18). (c) P(2.13 ≤ Z ≤ 2.57). (d) P(−2.3 ≤ Z ≤ −1.1). (e) P(0 ≤ Z ≤ 1.54). (f) P(−1.54 ≤ Z ≤ 1.54). (g) N(1.1243). (h) N(−1.1243).
1. A population random variable X has mean LaTeX: \mu=10μ = 10 and standard deviation LaTeX:...
1. A population random variable X has mean LaTeX: \mu=10μ = 10 and standard deviation LaTeX: \sigma=5σ = 5. Samples of size 36 are drawn with replacement. Find the probability that the sample mean LaTeX: \overline{X}X ¯ will be between 6.5 and 14, inclusive? 2. 52 percent of the voting population of a city favor candidate A for mayor. What is the probability that more than 51 percent will favor A in a random sample 50 voters from the city?
A normal random variable x has mean ? = 1.6 and standard deviation ? = 0.17....
A normal random variable x has mean ? = 1.6 and standard deviation ? = 0.17. Find the probability associated with each of the following intervals. (Round your answers to four decimal places.) (a)     1.00 < x < 1.20 (b)     x > 1.37 (c)     1.35 < x < 1.50
A normal random variable x has mean ? = 1.6 and standard deviation ? = 0.17....
A normal random variable x has mean ? = 1.6 and standard deviation ? = 0.17. Find the probability associated with each of the following intervals. (Round your answers to four decimal places.) (a)     1.00 < x < 1.30 (b)     x > 1.32 (c)     1.25 < x < 1.50
Suppose x is a random variable with a mean of 40 and a standard deviation of...
Suppose x is a random variable with a mean of 40 and a standard deviation of 6.5 that is not necessarily normally distributed. (a) If random samples of size n=20 are selected, can you say the sampling distribution of the means, the (x bar) distribution, is normally distributed? why or why not? (b) if random samples of size n=64 are selected, what can you say about the sampling distribution of the means, (x bar)? is it normally distributed? what is...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT