Question

The random variable x has a normal distribution with mean 23 and standard deviation 5. Find...

The random variable x has a normal distribution with mean 23 and standard deviation 5.

Find the value d such that P(20<X<d)=0.4641

Homework Answers

Answer #1

Solution

P( 20 < x < d ) = 0.4641

P[(20 - 23 )/ 5 ) < (x - ) /  < d) ] = 0.4641

= P(-0.60 < z < d) = 0.4641

= P(z < d) - P(z < -0.60) = 0.4641

Using z table,

=  P(z < d) - 0.2743 = 0.4641

=  P(z < d) = 0.4641 + 0.2743

=  P(z < d) = 0.7384

=  P(z < 0.64) = 0.7384

z = 0.64

Using z-score formula,

d = z * +

d = 0.64 * 5 + 23

d = 26.2

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Given a random variable X following normal distribution with mean of -3 and standard deviation of...
Given a random variable X following normal distribution with mean of -3 and standard deviation of 4. Then random variable Y=0.4X+5 is also normal. (1)Find the distribution of Y, i.e. μy,σy (2)Find the probabilities P(−4<X<0),P(−1<Y<0) (3)Find the probabilities(let n size =8) P(−4<X¯<0),P(3<Y¯<4) (4)Find the 53th percentile of the distribution of X
A random variable ?x has a Normal distribution with an unknown mean and a standard deviation...
A random variable ?x has a Normal distribution with an unknown mean and a standard deviation of 12. Suppose that we take a random sample of size ?=36n=36 and find a sample mean of ?¯=98x¯=98 . What is a 95% confidence interval for the mean of ?x ? (96.355,99.645)(96.355,99.645) (97.347,98.653)(97.347,98.653) (94.08,101.92)(94.08,101.92) (74.48,121.52)
Assume that x has a normal distribution with the specified mean and standard deviation. Find the...
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) ? = 4.6; ? = 1.9 P(3 ? x ? 6) = Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) ? = 28; ? = 4.2 P(x ? 30) = Consider a normal distribution with mean 36 and...
a.) Assume that x has a normal distribution with the specified mean and standard deviation. Find...
a.) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 4.4; σ = 2.2 P(3 ≤ x ≤ 6) = b.) Consider a normal distribution with mean 34 and standard deviation 2. What is the probability a value selected at random from this distribution is greater than 34? (Round your answer to two decimal places.) c.) Assume that x has a normal...
A random variable X follows a normal distribution with mean 135 and standard deviation 12. If...
A random variable X follows a normal distribution with mean 135 and standard deviation 12. If a sample of size 10 is taken, find P (x̅ < 137). (4 decimal places) Find the answer using StatCrunch.
If X is a normal random variable with a mean of 78 and a standard deviation...
If X is a normal random variable with a mean of 78 and a standard deviation of 5, find the following probabilities: a) P(X ≥ 78) (1 Mark) b) P(X ≥ 87) (1 Mark) c) P(X ≤ 91) (1 Mark) d) P(70 ≤ X ≤ 77) (1 Mark)
A. Assume that x has a normal distribution with the specified mean and standard deviation. Find...
A. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) ? = 6; ? = 2 P(5 ? x ? 8) = B. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) ? = 13.8; ? = 3.1 P(8 ? x ? 12) = C.Assume that x has...
a) Assume that x has a normal distribution with the specified mean and standard deviation. Find...
a) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 4; σ = 6 P(1 ≤ x ≤ 13) = b) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 103; σ = 20 P(x ≥ 120) = c) Find z such that 5%...
A: Let z be a random variable with a standard normal distribution. Find the indicated probability....
A: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(z ≤ 1.11) = B: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(z ≥ −1.24) = C: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(−1.78 ≤ z...
Let X have a normal distribution with a mean of 23 and a standard deviation of...
Let X have a normal distribution with a mean of 23 and a standard deviation of 5. Find P(X < 9 or X > 21) in the following steps (a) What region of the normal distribution are you looking to find the area of? (to the left of a zscore, to the right of a z-score, between two z-scores, or to the left of one z-score and to the right of another z-score) (b) Calculate the z-score(s) needed to find...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT