a. What is the frequency function (pmf) of X? b. Compute P(X > 10). c. Compute P( 6 ≤ X ≤ 10).

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Of all customers purchasing automatic garage door openers, 75% purchase chain-driven model. 
Let X = the number among the next 15 purchasers who select the chain-driven model.
a. What is the frequency function (pmf) of X?
b. Compute P(X > 10).
c. Compute P( 6 ≤ X ≤ 10).
d. Compute µ and σ2
e. If the store currently has in stock 10 chain-driven models and 8 shaft-driven models, what is the 
probability that at least 7 out of the 15 customers select a chain-driven model from this stock?

Expert Solution
Step 1

HERE AS PER POLICY I HAVE CALCULATED FIRST 3 SUBPART PLZ REPOST FOR REMAINING 

Of all customers purchasing automatic garage door openers, 75% purchase chain-driven model. 

Let X = the number among the next 15 purchasers who select the chain-driven model.

Here use binomial distribution 

  • Each trial independent 
  • Finite number of trial 
  • There are two outcomes success and failure 
  • Probability of success remains constant in each trial
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