Question

In: Statistics and Probability

Let X be normally distributed with mean μ = 18 and standard deviation σ = 8....

Let X be normally distributed with mean μ = 18 and standard deviation σ = 8. [You may find it useful to reference the z table.]

a. Find P(X ≤ 2). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

b. Find P(X > 4). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

c. Find P(8 ≤ X ≤ 16). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

d. Find P(12 ≤ X ≤ 22). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Expert Solution

a)

= P(Z < -2)

= 0.0228

b)

= P(Z > -1.75)

= 1 - P(Z < -1.75)

= 1 - 0.0401

= 0.9599

c)

= P(-1.25 < Z < -0.25)

= P(Z < -0.25) - P(Z < -1.25)

= 0.4013 - 0.1056

= 0.2957

d)

= P(-0.75 < Z < 0.5)

= P(Z < 0.5) - P(Z < -0.75)

= 0.6915 - 0.2266

= 0.4649

orchestra answered 2 years ago

Let X be normally distributed with mean μ = 18 and standard deviation σ = 14....

Let X be normally distributed with mean μ = 18 and standard deviation σ = 14. [You may find it useful to reference the z table.] a. Find P(X ≤ 4). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) b. Find P(X > 11). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) c. Find P(4 ≤ X ≤ 18). (Round "z" value to 2 decimal places and final...

Let X be normally distributed with mean μ = 26 and standard deviation σ = 13....

Let X be normally distributed with mean μ = 26 and standard deviation σ = 13. [You may find it useful to reference the z table.] a. Find P(X ≤ 0). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) b. Find P(X > 13). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) c. Find P(13 ≤ X ≤ 26). (Round "z" value to 2 decimal places and final...

Let X be normally distributed with mean μ = 146 and standard deviation σ = 34....

Let X be normally distributed with mean μ = 146 and standard deviation σ = 34. [You may find it useful to reference the z table.] a. Find P(X ≤ 100). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) b. Find P(95 ≤ X ≤ 110). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) c. Find x such that P(X ≤ x) = 0.330. (Round "z" value and...

Let X be normally distributed with mean μ = 20 and standard deviation σ = 12....

Let X be normally distributed with mean μ = 20 and standard deviation σ = 12. [You may find it useful to reference the z table.] a. Find P(X ≤ 2). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) b. Find P(X > 5). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) c. Find P(5 ≤ X ≤ 20). (Round "z" value to 2 decimal places and final...

Let X be normally distributed with mean μ = 3,800 and standard deviation σ = 2,000....

Let X be normally distributed with mean μ = 3,800 and standard deviation σ = 2,000. [You may find it useful to reference the z table.] a. Find x such that P(X ≤ x) = 0.9382. (Round "z" value to 2 decimal places, and final answer to nearest whole number.) b. Find x such that P(X > x) = 0.025. (Round "z" value to 2 decimal places, and final answer to nearest whole number.) c. Find x such that P(3,800...

Let X be normally distributed with mean μ = 4.1 and standard deviation σ = 3....

Let X be normally distributed with mean μ = 4.1 and standard deviation σ = 3. b. Find P(5.5 ≤ X ≤ 7.5). c. Find x such that P(X > x) = 0.0485.

et X be normally distributed with mean μ = 3.3 and standard deviation σ = 1.8....

et X be normally distributed with mean μ = 3.3 and standard deviation σ = 1.8. [You may find it useful to reference the z table.] a. Find P(X > 6.5). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) b. Find P(5.5 ≤ X ≤ 7.5). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) c. Find x such that P(X > x) = 0.0485. (Round "z" value and...

Assume that the random variable X is normally distributed, with mean μ=50 and standard deviation σ=7....

Assume that the random variable X is normally distributed, with mean μ=50 and standard deviation σ=7. compute the probability. P(57≤X≤66)

Let X be a random variable with mean μ and standard deviation σ. Consider a new...

Let X be a random variable with mean μ and standard deviation σ. Consider a new random variable Z, obtained by subtracting the constant μ from X and dividing the result by the constant σ: Z = (X –μ)/σ. The variable Z is called a standardised random variable. Use the laws of expected value and variance to show the following: a E(Z) = 0 b V (Z) = 1

Assume the random variable X is normally distributed with mean μ = 50 and standard deviation...

Assume the random variable X is normally distributed with mean μ = 50 and standard deviation σ = 7. Compute the probability. P(35<X<63)