According to the Bureau of Labor Statistics, in a recent month 26.0% of the total part-time workforce in the US was between the ages of 25 and 34. A random sample of 90 part-time employees was selected during this month. What is the probability that fewer than 19 people from the sample were between 25 and 34?

0.1177

Step-by-step explanation:

Given that:

p = 26% = 0.26 (probability of success)

Number of trials (samples) (n) = 90

Number of success (r) (people between 25 and 34) = less than 19

This is equivalent to;

p(0) + p(1) + p(2) + + p(18)

The binomial formula ;

P(n, x) = nCr * p^x * (1 - p)^(n-x)

Using the binomial distribution calculator :

P(90, 19) = 90C19 * p^x * (1 - p)^(n-x)

For x < 19;

p(0) + p(1) + p(2) + + p(18)

p(x < 19) = 0.1177