9. Let X ~ N(194; 24). Find:
(a) P(X <= 218)
(b) P(145 < X < 213)
(c) The first quartile for X
(d) The third quartile for X
(e) the IQR for X
(f) P(|X-194|> 41)
10. A soft drink machine discharges an average of 345 ml per
cup. The amount of drink is normally distributed with standard
deviation of 30 ml. What fraction of cups will contain more than
376 ml? (Keep 4 decimals)
Let X be a binomial random variable with n =
11 and p = 0.3. Find the following values. (Round your
answers to three decimal places.)
(a)
P(X = 5)
(b)
P(X ≥ 5)
(c)
P(X > 5)
(d)
P(X ≤ 5)
(e)
μ = np
μ =
(f) σ =
npq
σ =
Let X Geom(p). For positive integers n, k define
P(X = n + k | X > n) = P(X = n + k) / P(X > n) :
Show that P(X = n + k | X > n) = P(X = k) and then briefly
argue, in words, why this is true for geometric random
variables.
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)
1. Assume X ∼ N(20, 25),
(a) find P(X > 25)
(b) the value of x if P(X > x) = 0.975.
(c) find the values of a and b, two symmetrical values about 20
such that P(a < X < b) = 0.95.
(d) If X1, X2, . . . , X100 is random sample for the
distribution of X
• what is the sampling distribution of the sample mean X¯?
• find P(X >¯ 20.50)
(e) Suppose the...