SOLUTION: 1. A typist knows from previous experience that even though she is an experienced typist, she does make mistakes. Let X be the random variable representing the number of mistakes m

Algebra ->  Probability-and-statistics -> SOLUTION: 1. A typist knows from previous experience that even though she is an experienced typist, she does make mistakes. Let X be the random variable representing the number of mistakes m      Log On


   

Question 1086337: 1. A typist knows from previous experience that even though she is an experienced typist, she does make mistakes. Let X be the random variable representing the number of mistakes made by the typist on a randomly selected page from all those she has typed. The probability mass function of X is given below.
Number of mistakes x 0 1 2 3 4
Probability P(X = x) 0.3 (x) 0.15 0.08 0.02
a. The value of P(X = 1) is missing. What should it be?
b. What is the probability that a random selected page will have less than 2 mistakes?
c. What is the expected value of the random variable X?
d. What is the standard deviation of the random variable X?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You know that the sum of all probabilities must equal 1 so,
0.3%2Bx%2B+0.15%2B+0.08+%2B0.02=1
x=1-0.3-+0.15-+0.08+-0.02
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P%28X%3C2%29=P%280%29%2BP%281%29=0.3%2Bx
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E=sum%28x%2AP%28x%29%2Cx=1%2C4%29=0%2A0.3%2B1%2Ax%2B2%2A0.15%2B3%2A0.08%2B4%2A0.02
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Find the variance,

Then take the square root of the variance to get the standard deviation,
sigma=sqrt%28V%29