Suppose that the probability of getting an A in a paarticular course is 0.20, an

Question

Suppose that the probability of getting an A in a paarticular course is 0.20, and assume that the ail student grades are independent. If you randomly sample 10 students taking the course; Find the expected number of students out of the 10 that will get an A, and the standard deviation of number of students out of the 10 that will get an A. Find the probability that no student gets an A. Find the probability that at most 2 students get an A. Find the probability that more than the expected number of students get an A.

Explanation / Answer

a)

Here, n = 10, p = 0.20, so

u = mean = np =    2 [ANSWER, EXPECTED NUMBER]
  
s = standard deviation = sqrt(np(1-p)) =    1.264911064 [ANSWER, STANDARD DEVIATION]

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b)

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 =    10      
p = the probability of a success =    0.2      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.107374182 [ANSWER]

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c)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.2      
x = the maximum number of successes =    2      
          
Then the cumulative probability is          
          
P(at most   2   ) =    0.677799526 [ANSWER]

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d)

Note that P(more than x) = 1 - P(at most x).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.2      
x = our critical value of successes =    2      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   2   ) =    0.677799526
          
Thus, the probability of at least   3   successes is  
          
P(more than   2   ) =    0.322200474 [ANSWER]

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