alties that x may assume b What value of a is most probable

alties that x may assume. b. What value of a is most probable? c. Find the probability that x is less than 3. d, what is the probability that x = 3? e. Find and . 25 25) Based on past experiments, ski rental equipment at a university recreation facility is available 75% of the time. If a random sample of 15 time periods are selected, what is the probability that ski equipment is available a. exactly 10 times? b. at least 10 times? c. at most 10 times? p 0,15 d. fewer than 10 times? b p-

Solution

a)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    15      
p = the probability of a success =    0.75      
x = the number of successes =    10      
          
Thus, the probability is          
          
P (    10   ) =    0.165145981 [ANSWER]

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b)

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    15      
p = the probability of a success =    0.75      
x = our critical value of successes =    10      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   9   ) =    0.148368077
          
Thus, the probability of at least   10   successes is  
          
P(at least   10   ) =    0.851631923 [ANSWER]

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c)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    15      
p = the probability of a success =    0.75      
x = the maximum number of successes =    10      
          
Then the cumulative probability is          
          
P(at most   10   ) =    0.313514058 [ANSWER]

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d)

Note that P(fewer than x) = P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    15      
p = the probability of a success =    0.75      
x = our critical value of successes =    10      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   9   ) =    0.148368077
          
Which is also          
          
P(fewer than   10   ) =    0.148368077 [ANSWER]