Question

Statistics))

1.The Round-trip-time between the college and home for a student is normally distributed with a mean of 47 min and a standard deviation of 4.6 min. To one-decimal place, what Round-trip-time would be considered the 70th percentile? Make sure to include units.

2.A recent study showed that the average amount of time spent doing part time job by students at a college is 29 hours per week with a standard deviation of 3.8 hours. If 64 students were selected at random, what is the probability that their average weekly working hours will be less than 20 hours?Round answer to two decimals, if necessary.Express answer in percent. Don't forget to put % sign with you answer.

Answer 1

Solution:-

1) Given that,

mean = = 47

standard deviation = = 4.6

Using standard normal table,

P(Z < z) = 70%

= P(Z < z ) = 0.70

= P(Z < 0.52 ) = 0.70  

z = 0.52

Using z-score formula,

x = z * +

x = 0.52 * 4.6 + 47

x = 49.4 min.

2) Given that ,

mean = = 29

standard deviation = = 3.8

n = 64

=   = 29

= / n = 3.8/ 64 = 0.475

P( < 20) = P(( - ) / < (20 - 29) /0.475 )

= P(z < -18.95)

Using z table

= 0.00