Please help with the following STATISTIC problem, please show work!!!! A manufac
ID: 2923481 • Letter: P
Question
Please help with the following STATISTIC problem, please show work!!!!
A manufacturer claims that only 10% of its power supply units need service during the warranty period. If this claim is true, (a) What is the probability that of the 20 units sold 4 will need service during the 1. warranty period? (b) What is expected number of units that will need service? (c) What is the variance? 2. A fair die is rolled over and over until a 3 is rolled (a) What is the probability that it will take exactly four rolls? b) What is the expected value of this random variable? Interpret your answer. (c) What is the variance of this random variable? (d) What is the standard deviation of this random variable? 3. An oil company conducts a geological research and concludes that an exploratory oil well has 0.15 chance of striking oil. (a) What is the probability that the third strike comes in the sixth well drilled? (b) Determine the expected value and variance of this distribution. Interpret your answers 4. A bag contains twenty marbles: six red and fourteen black. Five marbles are drawn without replacement. What is the probability that exactly two are red? If electricity power failures occur according to a Poisson distribution with an average of three failures every twenty weeks, calculate the probability that there will not be more than one failure during a particular week. 5. ish (United States)Explanation / Answer
BIONOMIAL DISTRIBUTION
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 = 4 ) = ( 20 4 ) * ( 0.1^4) * ( 1 - 0.1 )^16
= 0.08978
b.
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 20 * 0.1
= 2
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 20 * 0.1 * 0.9
= 1.8
III.
standard deviation = sqrt( variance ) = sqrt(1.8)
=1.34164