Question

Problem 1. Let x be a random variable which approximately follows a normal distribution with mean µ = 1000 and σ = 200. Use the z-table, calculator, or computer software to find the following: Part A. Find P(x > 1500). Part B. Find P(x < 900). Part C. Find P(900 < x < 1500).

Answer #1

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...

Suppose that the random variable X follows a normal distribution
with mean 35 and variance 25.
a.) Calculate P(X > 37)
b.) Calculate P(32 < X < 38)
c.) Find the value of x so that P(X >x) is approximately
0.975

Let the random variable X follow a normal distribution with µ =
18 and σ = 4. The probability is 0.99 that X is in the symmetric
interval about the mean between two numbers, L and U (L is the
smaller of the two numbers and U is the larger of the two numbers).
Calculate L.

Let the random variable X follow a normal distribution
with µ = 22 and σ = 4. The probability is 0.90
that Xis in the symmetric interval about the mean between
two numbers, L and U (L is the smaller of the two numbers and U is
the larger of the two numbers). Calculate U.

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.

Let the random variable X follow a normal distribution with µ =
19 and σ2 = 8. Find the probability that X is greater than 11 and
less than 15.

Let the random variable X follow a normal distribution with µ =
18 and σ2 = 11. Find the probability that X is greater than 10 and
less than 17.

Let 'x' be a random variable that represents the length of time
it takes a student to write a term paper for Tonys class. After
interviewing students, it was found that 'x' has an approximately
normal distribution with a mean of µ = 7.3 hours and standard
deviation of ơ = 0.8 hours.
For parts a, b, c, Convert each of the following x
intervals to standardized z intervals.
a.) x < 7.5
z <
b.) x > 9.3
z...

Suppose X is a normal random variable with mean μ = 5 and P(X
> 9) = 0.2005.
(i) Find approximately (using the Z-table) what is Var(X).
(ii) Find the value c such that P(X > c) = 0.1.

Suppose the random variable X follows a normal distribution with
mean μ=52 and standard deviation σ=10.
Calculate each of the following.
In each case, round your response to at least 4 decimal
places.
a) P(X < 41) =
b) P(X > 61) =
c) P (47 < X < 67) =

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