A particular type of tennis racket comes in a midsize versio

A particular type of tennis racket comes in a midsize version and an oversize version. Sixty percent of all customers at a certain store want the oversize version. (Round your answers to three decimal places.)

(b) Among ten randomly selected customers, what is the probability that the number who want the oversize version is within 1 standard deviation of the mean value?

(c) The store currently has seven rackets of each version. What is the probability that all of the next ten customers who want this racket can get the version they want from current stock?

Solution

b)

u = mean = np =    6
  
s = standard deviation = sqrt(np(1-p)) =    1.549193338

Hence, the question is asking P(5<=x<=7).

Note that P(between x1 and x2) = P(at most x2) - P(at most x1 - 1)          
          
Here,          
          
x1 =    5      
x2 =    7      
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.6      
          
Then          
          
P(at most    4   ) =    0.166238618
P(at most    7   ) =    0.832710246
          
Thus,          
          
P(between x1 and x2) =    0.666471629   [ANSWER]

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c)

There must be at least 3 but at most 7 who want oversize.

Note that P(between x1 and x2) = P(at most x2) - P(at most x1 - 1)          
          
Here,          
          
x1 =    3      
x2 =    7      
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.6      
          
Then          
          
P(at most    2   ) =    0.012294554
P(at most    7   ) =    0.832710246
          
Thus,          
          
P(between x1 and x2) =    0.820415693   [ANSWER]