Statistics homework

Question

A national study found that college students with jobs worked an average of 22 hours per week. The standard deviation is 9 hours. A college student with a job is selected at random. Find the probability that the student works for less than 4 hours per week. Assume that the lengths of time college student’s work are normally distributed and are represented by the variable X

show all steps

Answer 1

mean = 22 SD = 9

want to find P(x < 4)

convert limit 4 to standardized (z) by subtraction mean and dividing by standard deviation:

P(x < 4) = P(z < (4 - 22)/9) = P(z < -2) = 0.0228