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Using the Binomial Probability Distribution Function

 

Example:  According to Nielsen Media Research, 75% of all United States households have cable television.

 

(a) In a random sample of 15 households, what is the probability that exactly 10 have cable?

 

(b) In a random sample of 15 households, what is the probability that at least 13 have cable?

 

(c) In a random sample of 15 households, what is the probability that fewer than 13 have cable?

 

(a.) To find the probability that exactly 10 households have cable, we will use the binomial probability density function, binompdf(n,p,x). For this example, n= 15, p = .75 and x = 10. Press 2nd [DISTR.] . Scroll down through the menu to select 0: binompdf( and press ENTER. Type in 15, .75 , 10) and press ENTER. The answer, .1651, will appear on the screen.

 

 

(b.-c.) To calculate inequalities, such as the probability that at least 13 households have cable, , or the probability that fewer than 13 household have cable, , you can use the cumulative probability command: binomcdf (n,p,x). This command accumulates probability starting at X = 0 and ending at a specified X-value.

 

To calculate , press 2nd [DISTR] and select A:binomcdf ( by scrolling through the options and selecting A:binomcdf( or pressing ALPHA A. (Note: A is the ALPHA function on the MATH key. ) Type in 15 , .75 , 12, ) and press ENTER. The result, . This value is the complement of . Subtract this value from 1 to obtain

 

is the same as .