The police department of a major city needs to update its budget. for this purpose, they need to understand the variation in their fines collected from motorists for speeding. as a sample, they recorded the speeds of cars driving past a location with a 35 mph speed limit, a place that in the past has been known for producing fines. the mean of 100 representative readings was 38.74 mph, with a standard deviation of 3.31 mph. a) how many standard deviations from the mean would a car going the speed limit be? b) which would be more unusual, a car traveling 48 mph or one going 25 mph?

a) - 1.13

b) The speed of 25 mph is more unusual.

Step-by-step explanation:

Given:

Speed limit = 35 mph

Mean of speeds, μ = 38.74 mph

standard deviation, σ = 3.31 mph

a) Now,

thus,

for x = 35 mph

here,

z is the deviation from the mean

or

z = - 1.129 ≈ - 1.13

b) now,

for x = 48

or

z = 2.79

and, for x = 25 mph

or

z = -4.15

on comparing the results we can see that 25 mph is more deviated from the mean, thus the speed of 25 mph is more unusual.

step-by-step explanation:

because it just is

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)