Question

Given X has a normal distribution, could you find a probability for x bar if n was only 10, why or why not?

Answer #1

Yes, we can find the probability for x bar

From Central Limit Theorem, if the population follows Normal distribution, the sampling distribution of the sample mean also follows Normal distribution irrespective of the sample size

Thus, x bar will have mean equal to the population mean and standard deviation equal to where is the population standard deviation

Now, we can calculate the Corresponding z value and get the required probability from Standard normal distribution table

X has a normal distribution with the given mean and
standard deviation. Find the indicated probability. (Round your
answer to four decimal places.)
μ = 39, σ = 20, find
P(32 ≤ X ≤ 49)

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given that μ = 14.9 and σ = 4.0. (Use 4 decimal places.)
b.) Let z be a random variable with a standard normal
distribution. Find P(–1.13 ≤ z ≤ 2.47). Use 4
decimal places.
c.) Consider a normal distribution with mean 25 and standard
deviation 5. What is the probability that a value selected at
random from this distribution is greater than 25? (Use 2...

Assume that x has a normal distribution, and find the indicated
probability.
1) The mean is 15.2 and the standard deviation is 0.9. Find the
probability that x is greater than 17.
2) Let x be a continuous random variable that follows a normal
distribution with a mean of 17.3 and a standard deviation of 3.2.
Find the value of x so that the area under the normal curve to the
left of x is .500.
Please show all the...

X has a normal distribution with the given mean and a standard
deviation. Find the indicated probability. (Round your answer to
four decimal places.) μ = 108, σ = 15, find P(111 ≤ X ≤ 129)

Use Excel functions to find the following probability of Normal
distribution
a.) P (X > 70) when X ~ N (65, 10)
b.) P(20 < X < 40) when X ~ N (32, 12)

Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X≥10) P ( X ≥ 10 ) , n=14 , p=0.8

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obtaining a success. Round your answer to four decimal places.
P(X≥7), n=10, p=0.5

Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X≥10), n=14, p=0.8

Given That X has a normal distribution with — 54 and = 5,
find
< 43.2)
> 66.2)
P(60.4 < x < 65.6)
Find such that P(x < f) .0146

Assume that X has a normal distribution, and find the
indicated probability.
The mean is μ = 15.2 and the standard deviation is σ =
0.9.
Find the probability that X is between 14.3 and 16.1.
Group of answer choices
0.6826
0.8413
0.3413
0.1587

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