Find the following probabilities for the standard normal random
variable z z :
a) P(−2.07≤z≤1.93)= P ( − 2.07 ≤ z ≤ 1.93 ) =
(b) P(−0.46≤z≤1.73)= P ( − 0.46 ≤ z ≤ 1.73 ) =
(c) P(z≤1.44)= P ( z ≤ 1.44 ) =
(d) P(z>−1.57)= P ( z > − 1.57 ) =
Let z be a random variable with a standard normal
distribution.
Find “a” such that P(|Z| <A)= 0.95
This is what I have:
P(-A<Z<A) = 0.95
-A = -1.96
How do I use the symmetric property of normal distribution to make
A = 1.96?
My answer at the moment is P(|z|< (-1.96) = 0.95
Let X represent a binomial random variable with
n = 110 and p = 0.19. Find the following
probabilities. (Do not round intermediate calculations.
Round your final answers to 4 decimal places.)
a.
P(X ≤ 20)
b.
P(X = 10)
c.
P(X > 30)
d.
P(X ≥ 25)
Let X represent a binomial random variable with n = 180 and p =
0.23. Find the following probabilities. (Do not round intermediate
calculations. Round your final answers to 4 decimal places.)
a. P(X less than or equal to 45)
b. P(X=35)
c. P(X>55)
d. P (X greater than or equal to 50)
Let X represent a binomial random variable with n = 380 and p =
0.78. Find the following probabilities. (Round your final answers
to 4 decimal places.) Probability a. P(X ≤ 300) b. P(X > 320) c.
P(305 ≤ X ≤ 325) d. P( X = 290)
Let z be a random variable with a standard normal distribution.
Find P(0 ≤ z ≤ 0.46), and shade the corresponding area under the
standard normal curve. (Use 4 decimal places.)
1) Let X be a normally distributed random variable with a standard deviation equal 3; i.e. X∼N(μ, σ=3. Someone claims that μ=13. A random sample of 16 observations generate a sample mean of 14.56.
a) Does the sample mean provide evidence against the above claim at 5% significance level?
Complete the four steps of the test of hypothesis:
b) Assume that X was not normal; for example, X∼Unifμ-3, μ+3 which would have the same standard deviation. Use simulation to...
Let X be a standard normal random variable so that X N(0; 1).
For this problem you may
want to refer to the table provided on Canvas. Recall, that (x)
denotes the standard normal
CDF.
(a) Find (1:45).
(b) Find x, such that (x) = 0:4.
(c) Based on the fact that (1:645) = 0:95 nd an interval in which X
will fall with 95%
probability.
(d) Find another interval (dierent from the one in (c)) into which
X will...
1.
(Use Computer) Let X represent a binomial random
variable with n = 400 and p = 0.8. Find the
following probabilities. (Round your final answers to 4
decimal places.)
Probability
a. P(X ≤ 330)
b. P(X > 340)
c. P(335 ≤ X ≤ 345)
d. P(X = 300)
2.
(Use computer) Suppose 38% of recent college graduates plan on
pursuing a graduate degree. Twenty three recent college graduates
are randomly selected.
a.
What is the...