TOIE When 1 call, OLord; be merciful to me and answer me.\" Label each of the fo
ID: 3050474 • Letter: T
Question
TOIE When 1 call, OLord; be merciful to me and answer me." Label each of the following as either true (T) or false (F) (2 pt. ea.) 1. T Two events are mutually exclusive if they cannot occur at the same time. If two events are mutually exclusive, then they are also independent. If two events are independent, then they are also mutually exclusive. The law of large numbers says that as the sample size increases the relative The formula for the mean of a binomial variable can be written as -np. The complement of the event getting at least one correct answer out of ten, is 2. 3. 4 frequency probability approaches the theoretical probability value. 6. getting at most one correct answer out of ten. The formula for the mean of a geometric variable can be written as 8. If events A and B are independent, then P(A) - P(A/B). the following multiple choice questions, choose the answer that best fits the question. (2 pt. ea.) 9. If a probability experiment is conducted, which of the following cannot be nsidered a probability of an outcome? a) 2/5 b) 4/7 10. Distribution? Which of the following characteristics is not a characteristic of a Binomial a) The probability of success does not change from trial to trial. b) It is a discrete distribution. c) It has two equally likely outcomes. d) It has a fixed number of trials.Explanation / Answer
Q25.
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
a.
P( X = 10 ) = ( 20 10 ) * ( 0.5^10) * ( 1 - 0.5 )^10
= 0.176197
b.
P( X < 12) = P(X=11) + P(X=10) + P(X=9) + P(X=8) + P(X=7) + P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(x=1)+P(X=0)
= ( 20 11 ) * 0.5^11 * ( 1- 0.5 ) ^9 + ( 20 10 ) * 0.5^10 * ( 1- 0.5 ) ^10 + ( 20 9 ) * 0.5^9 * ( 1- 0.5 ) ^11 + ( 20 8 ) * 0.5^8 * ( 1- 0.5 ) ^12 + ( 20 7 ) * 0.5^7 * ( 1- 0.5 ) ^13 + ( 20 6 ) * 0.5^6 * ( 1- 0.5 ) ^14 + ( 20 5 ) * 0.5^5 * ( 1- 0.5 ) ^15 + ( 20 4 ) * 0.5^4 * ( 1- 0.5 ) ^16 + ( 20 3 ) * 0.5^3 * ( 1- 0.5 ) ^17 + ( 20 2 ) * 0.5^2 * ( 1- 0.5 ) ^18 + ( 20 1 ) * 0.5^1 * ( 1- 0.5 ) ^19 + ( 20 0 ) * 0.5^0 * ( 1- 0.5 ) ^20
= 0.748278
P( X > = 12 ) = 1 - P( X < 12) = 0.251722
c.
P( X < 5) = P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 20 4 ) * 0.5^4 * ( 1- 0.5 ) ^16 + ( 20 3 ) * 0.5^3 * ( 1- 0.5 ) ^17 + ( 20 2 ) * 0.5^2 * ( 1- 0.5 ) ^18 + ( 20 1 ) * 0.5^1 * ( 1- 0.5 ) ^19 + ( 20 0 ) * 0.5^0 * ( 1- 0.5 ) ^20 +
= 0.005909
Q26.
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 79
standard Deviation ( sd )= 5
a.
P(X = 87) = (87-79)/5
= 8/5= 1.6
b.
P(X < 70) = (70-79)/5
= -9/5= -1.8
= P ( Z <-1.8) From Standard Normal Table
= 0.0359
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