If 60 of all women are employed outside the home find the f

If 60 % of all women are employed outside the home, find the following probabilities. If sample of 8 women are selected, what is the probability that less than 3 women are employed If a sample of n 80 women selected, what is the probability that less than 42 women are employed

Solution

1.

Note that P(fewer than x) = P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    8      
p = the probability of a success =    0.6      
x = our critical value of successes =    3      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   2   ) =    0.04980736
          
Which is also          
          
P(fewer than   3   ) =    0.04980736 [ANSWER]

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2.

Note that P(fewer than x) = P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    80      
p = the probability of a success =    0.6      
x = our critical value of successes =    42      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   41   ) =    0.069921686
          
Which is also          
          
P(fewer than   42   ) =    0.069921686 [ANSWER]