Question

In: Statistics and Probability

A normal distribution has μ = 32 and σ = 5. (a) Find the z score...

A normal distribution has μ = 32 and σ = 5.

(a) Find the z score corresponding to x = 27.

(b) Find the z score corresponding to x = 45.

(c) Find the raw score corresponding to z = −3.

(d) Find the raw score corresponding to z = 1.3.

Expert Solution

Solution :

Given that,

mean = = 32

standard deviation = = 5

(a)

x = 27

z = x - / = 27 - 32 / 5 = -1

z score = -1

(b)

x = 45

z = x - / = 45 - 32 / 5 = 2.6

z score = 2.6

(c)

z = -3

Using z-score formula,

x = z * +

x = -3 * 5 + 32 = 17

raw score = 17

(d)

z = 1.3

Using z-score formula,

x = z * +

x = 1.3 * 5 + 32 = 38.5

raw score = 38.5

orchestra answered 2 years ago

A normal distribution has μ = 30 and σ = 5. (a) Find the z score...

A normal distribution has μ = 30 and σ = 5. (a) Find the z score corresponding to x = 25. b) Find the z score corresponding to x = 42. (c) Find the raw score corresponding to z = −2. (d) Find the raw score corresponding to z = 1.9.

Assume a normal distribution with μ = 0 and σ = 1, find the z-score(s) for...

Assume a normal distribution with μ = 0 and σ = 1, find the z-score(s) for each statement below: a) the area is 0.4 to the left of z b) the area is 0.18 to the right of z c) the middle area is 0.31 between −z and z __________________________ The heights of a certain population of corn plants follow a distribution with a mean of 137 cm and a standard deviation 23.19 cm. Find the raw scores for the...

Suppose x has a normal distribution with mean μ = 32 and standard deviation σ =...

Suppose x has a normal distribution with mean μ = 32 and standard deviation σ = 12. Describe the distribution of x values for sample size n = 4. (Round σx to two decimal places.) μx = Incorrect: Your answer is incorrect. σx = Describe the distribution of x values for sample size n = 16. (Round σx to two decimal places.) μx = σx = Describe the distribution of x values for sample size n = 100. (Round σx...

A normal distribution has a mean of μ = 80 with σ = 12. Find the...

A normal distribution has a mean of μ = 80 with σ = 12. Find the following probabilities. (a) p(X > 83) (b) p(X < 74) (c) p(X < 92) (d) p(71 < X < 89)

Consider a normal population with μ = 40 and σ = 4.2. Calculate the z-score for...

Consider a normal population with μ = 40 and σ = 4.2. Calculate the z-score for an x of 49 from a sample of size 15. (Give your answer correct to two decimal places

uestion 5 (1 point) If μ=5.06 and σ=1.27, find the z-score for x=6.87. Question 5 options:...

uestion 5 (1 point) If μ=5.06 and σ=1.27, find the z-score for x=6.87. Question 5 options: 1.43 2.89 -1.43 -2.89 Question 6 (1 point) If μ=63.81 and σ=7.94, find the z-score for x=50.16. Question 6 options: -1.72 -1.719 1.72 1.719 Question 7 (1 point) Use the following set of sample values to answer the question. 33 36 27 30 35 25 19 23 36 10 20 23 13 21 16 37 26 37 12 32 What is the IQR (interquartile...

Given a normal distribution with μ=40 and σ =9, find (a) the normal curve area to...

Given a normal distribution with μ=40 and σ =9, find (a) the normal curve area to the right of x=25; (b) the normal curve area to the left of x=29; (c) the normal curve area between x=43 and x=52; (d) the value of x that has 90% of the normal curve area to the left; and (e) the two values of x that contain the middle 70% of the normal curve area.

Given a normal distribution with μ=40 and σ=66, find (a) the normal curve area to the...

Given a normal distribution with μ=40 and σ=66, find (a) the normal curve area to the right of x=24; (b) the normal curve area to the left of x=29; (c) the normal curve area between x=47 and x=54; (d) the value of x that has 70% of the normal curve area to the left; and (e) the two values of x that contain the middle 65% of the normal curve area.

A normal distribution has a mean of µ = 28 with σ = 5. Find the...

A normal distribution has a mean of µ = 28 with σ = 5. Find the scores associated with the following regions: a. the score needed to be in the top 41% of the distribution b. the score needed to be in the top 72% of the distribution c. the scores that mark off the middle 60% of the distribution

Let z denote a random variable having a normal distribution with μ = 0 and σ...

Let z denote a random variable having a normal distribution with μ = 0 and σ = 1. Determine each of the probabilities below. (Round all answers to four decimal places.) (a) P(z < 0.2) = (b) P(z < -0.2) = (c) P(0.40 < z < 0.86) = (d) P(-0.86 < z < -0.40) = (e) P(-0.40 < z < 0.86) = (f) P(z > -1.24) = (g) P(z < -1.5 or z > 2.50) =