Question

Assume that x has a normal distribution, and find the indicated probability. 1) The mean is...

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 work. Thank you.

Homework Answers

Answer #1

Solution :

Given that ,

1)

mean = = 15.2

standard deviation = = 0.9

P(x > 17) = 1 - P(x < 17)

= 1 - P((x - ) / < (17 - 15.2) / 0.9)

= 1 - P(z < 2)

= 1 - 0.9772   

= 0.0228

Probability = 0.0228

2)

P( Z < z ) = 0.500

P(Z < 0 ) = 0.500

z = 0

Using z-score formula,

X = z* +

= 0*3.2 + 17.3

= 17.3

The value of X is 17.3

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
Assume that X has a normal distribution, and find the indicated probability. The mean is μ...
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
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%...
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: 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...
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...
Let z be a random variable with a standard normal distribution. Find the indicated probability. (Enter...
Let z be a random variable with a standard normal distribution. Find the indicated probability. (Enter a number. Round your answer to four decimal places.) P(z ≥ 1.41) = Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Enter a number. Round your answer to four decimal places.) The area between z = 0.41 and z = 1.82 is .
__________ For a continuous random variable x, the area under the probability distribution curve between any...
__________ For a continuous random variable x, the area under the probability distribution curve between any two x-values is always _____. Greater than 1    B) less than zero    C) equal to 1    D) in the range zero to 1, inclusive _________For a continuous random variable x, the total area under the probability distribution curve of x is always ______? Less than1          B) greater than 1              C) equal to 1                      D) 0.5 ___________ The probability that a continuous random variable x...
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.) μ = 14.6; σ = 3.2 P(8 ≤ x ≤ 12) =
1)     let X be a continuous random variable that has a normal distribution with a mean...
1)     let X be a continuous random variable that has a normal distribution with a mean of 40 and a standard  deviation of 5. Find the probability that X assumes a value:        a. between 32 and 35   b. between 41 and 50        c. greater than 43     d. less than 49
1. Assume that x has a normal distribution with the specified mean and standard deviation. Find...
1. 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 = 14.3; σ = 3.5 P(10 ≤ x ≤ 26)=? 2.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 = 5.9; σ = 1.1 P(7 ≤ x ≤ 9)=? 3. Assume that x has a normal...