Jorie normally leaves work at 5: 00 pm, but she is leaving work 30 minutes late today. she decides to make up time by taking the toll road instead of side
streets. she can travel four times faster by taking the toll road. create an equation in terms of x to represent the number of minutes after 5: 00 pm she
arrives home from work if she leaves late. let x represent the number of minutes her normal commute takes when she leaves on time.
y = -x-30
y = 4x - 30
y = -x +30
y = 4x + 30

answer: true

step-by-step explanation:

cross multiplying, we get :

⇒ (3) × (5) = (9) × (x)

⇒ 15 = 9x

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.