Binomial Probability Question

Question

In 2009, a study from a consumer research company reported that 54% of teenagers sent a text message on their cell phone during the past 30 days. A sample of 15 teenagers is studied. Round the answers to four decimal places.

What is the probability that six or more sent a text message?

I know how to start this problem by using the binomial formula which will be P(Less than or equal to 5)= P(0)+P(1)+P(2)+P(3)+P(4)+P(5)

=15C0(0.54)^0(1-0.54)^15 onward

however, when I check the examples my homework provides alongside trying other similar problems, I get different values for my computations and the answer is marked wrong.

Any help will be appreciated!

Answer 1

The answer is 91.1%

I did it using MS Excel by creating the table which contains

the columns:

x=6,7,8,9,10,11,12,13,14,15

(N choose x)

0.54^x

(0.46)^(N-x)

The probabilities are calculated using the formula (N choose x) * 0.54^x * (0.46)^(N-x)

for x = 6,7,8,9,....,13,14,15

I also did the normal approximation to the binomial, where mean = 15*0.54 and

std dev = sqrt( 15 * 0.54 * 0.46)

You then convert them to z-scores and use the normal table.

The spreadsheet is called Binomial Normal Approx.xls and is uploaded to the resources page.