Suppose X is a normal random variable with μ = 350 and σ = 40. Find...

Suppose X is a normal random variable with μ = 350 and σ = 40. Find the values of the following probabilities. (Round your answers to four decimal places.)

(a) P(X < 468)

(b) P(390 < X < 454)

(c) P(X > 390)

Expert Solution

Given that X is a normal random variable with μ = 350 and σ = 40. hence the probability is calculated busing Z statistics.

a) P(X < 468) is calculated by finding the Z score at X = 468 as:

Thus P(X<468) =P(Z<2.95) is calculated using excel formula for norma distribution which is =NORM.S.DIST(2.95, TRUE), thus the probability computed is 0.9984.

b) P(390 < X < 454)

The Z scores are:

so, P(390 < X < 454) = P(1<Z<2.6) = P(X<2.6) -P(Z<1) is calculated using excel formula for normal distribution which is =NORM.S.DIST(2.6,TRUE)-NORM.S.DIST(1,TRUE), thus P(390 < X < 454) is computed from formula as 0.1540.

(c) P(X > 390), the Z score to calculated the probability is :

Thus P(X>390) =P(Z>1) is calculated using excel formula for normal distribution which is =1-NORM.S.DIST(1,TRUE), thus results in P(X>390) = 0.1587.

orchestra answered 1 year ago

Suppose X is a normal random variable with μ = 600 and σ = 89. Find...

Suppose X is a normal random variable with μ = 600 and σ = 89. Find the values of the following probabilities. (Round your answers to four decimal places.) (a) P(X < 700) (b) P(X > 350) (c) P(300 < X < 900)

For a normal random variable, with μ = 19, and σ = 6, find the following...

For a normal random variable, with μ = 19, and σ = 6, find the following probabilities. (a) Pr(X ≤ 32.2) (b) Pr(X > 4.00)

Suppose x has a distribution with μ = 40 and σ = 15. (a) If random...

Suppose x has a distribution with μ = 40 and σ = 15. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? Yes, the x distribution is normal with mean μx = 40 and σx = 15.Yes, the x distribution is normal with mean μx = 40 and σx = 0.9. Yes, the x distribution is normal with mean μx = 40 and σx = 3.75.No, the sample...

Suppose x is a normally distributed random variable with μ=13 and σ=2. Find each of the...

Suppose x is a normally distributed random variable with μ=13 and σ=2. Find each of the following probabilities. (Round to three decimal places as needed.) a) P(x ≥14.5) b) P(x12.5) c) P(13.86 ≤ x ≤ 17.7) d) P(7.46 ≤ x ≤16.52) d) c)

Suppose x is a normally distributed random variable with μ=30 and σ=5. Find a value of the...

Suppose x is a normally distributed random variable with μ=30 and σ=5. Find a value of the random variable x. (Round to two decimal places as needed.) p(x >): 0.95

A normal random variable x has mean μ = 1.8 and standard deviation σ = 0.18....

A normal random variable x has mean μ = 1.8 and standard deviation σ = 0.18. Find the probabilities of these X-values. (Round your answers to four decimal places.) (a) 1.00 < X < 1.50 (b) X > 1.39 (c) 1.45 < X < 1.60

1) A normal random variable x has an unknown mean μ and standard deviation σ =...

1) A normal random variable x has an unknown mean μ and standard deviation σ = 2. If the probability that x exceeds 4.6 is 0.8023, find μ. (Round your answer to one decimal place.) μ = 2) Answer the question for a normal random variable x with mean μ and standard deviation σ specified below. (Round your answer to four decimal places.) μ = 1.3 and σ = 0.19. Find P(1.50 < x < 1.71). P(1.50 < x <...

Given a random variable X having a normal distribution with μ=50, and σ =10. The probability...

Given a random variable X having a normal distribution with μ=50, and σ =10. The probability that Z assumes a value between 45 and 62 is: ___________.

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.

Question