Question

Teen drives (those aged 15-19) spend an average of 25 minutes behind the wheel each day. Assume that the standard deviation is known to be 7.6 minutes. You randomly select 35 teenage drivers

1. Can you use the normal model to describe the sampling distrubiton of sample means?

b. what is the mean of the sampling distribution

c. What is the standard deviation of the sampling distribution

d. You take a random sample of 35 teen drivers and want to find the probabilty that the mean time they spend driving each day is less than 21.5 minutes. What z-score should you use?

e. You take a random sample of 35 teen drives. What is the probability that the mean time they spend driving each day is less than 21.5 minutes?

Answer 1

Solution :

Given that ,

mean = = 25 minutes

standard deviation = = 7.6 minutes

n = 35

1) yes, the sampling distribution is approximately normal ,because sample size greater than 30

b) =   = 25 minutes

c) = / n = 7.6 / 35 = 1.285

d) = 21.5

z = -   /

z = 21.5 -25 / 1.285

z = -2.72

e) P( < 21.5 ) = P(( - ) / < (21.5 - 25) / 1.285 )

= P(z < -2.72)

Using z table

= 0.0033