Assuming a random variable X is distributed with a mean of the second digit of your...

Assuming a random variable X is distributed with a mean of the second digit of your student number, a variance of the last digit of your student number divided by 10 ( if the last digit is zero, use 9).

If you take 64 independent samples from X, what is the probability that the sample means is greater than 5?
The sample mean that you get from the previous sample is 3.5; please construct a 95% confidence interval based on the previous assumption.
Interpret the confidence interval that you constructed.
Based on your sample results that the sample mean is 3.5, assuming you do not know the true populations mean, test the hypothesis that the population mean of X equals to the third digit of your student number. Do you reject or nor reject your hypothesis?
Do you think you might have made mistake in your conclusion in step D? Why?
If you increase your sample size to 100, would the conclusion in step D change? Why and why not?

Expert Solution

orchestra answered 1 year ago

X is a random variable which is normally distributed with a mean of 99.01 and a...

X is a random variable which is normally distributed with a mean of 99.01 and a standard deviation of 15.56. Use the Excel function NORMINV to determine the required value of Xo to two decimal places. Give your answer in the form xx.xx. P(X < Xo) = 0.0344 Answer:

Let x be a continuous random variable that is normally distributed with a mean of 65...

Let x be a continuous random variable that is normally distributed with a mean of 65 and a standard deviation of 15. Find the probability that x assumes a value: less than 48 greater than 87 between 56 and 70

5. X is a normally distributed random variable with a mean of 8 and a standard...

5. X is a normally distributed random variable with a mean of 8 and a standard deviation of 3. The probability that X is between 6 and 10 is a. 0.7486 b. 0.4972 c. 0.6826 d. 0.8413 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 20 pounds. 6. The probability of a player weighing more than 240 pounds is a. 0.0197 b. 0.9803 c. 0.4803 d. 0.0228 7. Refer...

The random variable x is normally distributed with a mean of 68 and a standard deviation...

The random variable x is normally distributed with a mean of 68 and a standard deviation of 4. Find the interquartile range (IQR)? Use R.

A random variable X is exponentially distributed with a mean of 0.21. a-1. What is the...

A random variable X is exponentially distributed with a mean of 0.21. a-1. What is the rate parameter λ? (Round your answer to 3 decimal places.) a-2. What is the standard deviation of X? (Round your answer to 2 decimal places.) b. Compute P(X > 0.36). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

1. Given that the random variable X is normally distributed with a mean of 30 and...

1. Given that the random variable X is normally distributed with a mean of 30 and a standard deviation of 5, determine the following: P(32.2 <X). 2. The pdf(probability distribution function) of a random variable X is given by f(x) = 3x^2 with support 0<x<1. Determine P(0.4 < X < 0.6).

Suppose that y = x2, where x is a normally distributed random variable with a mean

Suppose that y = x2, where x is a normally distributed random variable with a mean and variance of µx = 0 and σ2x = 4. Find the mean and variance of y by simulation. Does µy = µ2x? Does σy = σ2x? Do this for 100, 1000, and 5000 trials.

Question 1: Assume that the random variable X is normally distributed, with mean that = 47...

Question 1: Assume that the random variable X is normally distributed, with mean that = 47 and standard deviation that = 7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(X< AND = TO 43) Using technology, what is P(X< AND = TO 43) equal? (round to four decimal places) How did you find this answer using a graphing calculator?? Question 2: The mean incubation time for a type of...

A random variable X is Normally distributed with mean = 75 and = 8. Let Y...

A random variable X is Normally distributed with mean = 75 and = 8. Let Y be a second Normally distributed random variable with mean = 70 and = 12. It is also known that X and Y are independent of one another. Let W be a random variable that is the difference between X and Y (i.e., W = X – Y). What can be said about the distribution of W?

Assume that the random variable x is normally distributed with mean μ = 70 and standard...

Assume that the random variable x is normally distributed with mean μ = 70 and standard deviation σ = 10. Find P(x < 82) a. 0.9942 b. 0.4500 c. 0.1151 d. 0.8849

Question