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A quiz worth 5 points is given to a statistics class. Let X represent the score

ID: 3207763 • Letter: A

Question

A quiz worth 5 points is given to a statistics class. Let X represent the score of a randomly selected student in the class. The probability distribution for X is given below.

Find the missing value, K.

Find the standard deviation of the score.

Round your answer to 4 decimal places.

WidgCo is a company that manufactures widgets. It is known that 1 out of every 49 widgets that the company produces is defective. A batch of 150 widgets is produced.

Find the probability that the number of defective widgets is exactly 5.

Round your answer to 4 decimal places.

x 0 1 2 3 4 5 P(x) 0.06 0.12 0.19 0.21 K 0.15

Explanation / Answer

Binomial 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
X ~ B ( 150, 1/49)
X ~ B ( 150, 0.0204082)
P( X = 5 ) = ( 150 5 ) * ( 0.0204082^5) * ( 1 - 0.0204082 )^145
= 0.1053