You are the manager of a car rental company. You are preparing an annual report about the travelling distance and the rental cost of the rented cars in the daily rental department. According to the record, the
daily travelling distance of a rented car follows a normal distribution with mean 40 km and standard deviation
8 km. The daily rental cost of a car is calculated as $3 per km of the traveling distance plus an additional
service charge of $30.
(a) What is the probability that the travelling distance of a rented car in a day is more than 50 km?
(b) There is 33% chance that the travelling distance of a rented car in a day is less than D km. What is the
value of D?
(c) Find the mean and standard deviation of the daily rental cost.
(d) The senior manager suggests a promotion that fix the maximum daily rental cost at $200. Suppose there
is no change in the distribution of the travelling distance due to this promotion. What percentage of
daily car rents would be benefit by this promotion?

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

move it to the other side

step-by-step explanation: