Question

In 2019, the amount of money that motorists spent on gas had a normal distribution with a mean of $900 and a standard deviation of $100. (a) Find the probability that a motorist spent more than $835 on gas. (b) Find the probability that a motorist spent between $828 and $942 on gas. (c) 75% of motorists spent less than what amount on gas? (d) Between what two amounts symmetrically distributed about the mean did 70% of motorists spend on gas?

Answer 1

Solution-:

Let, X- the amount of money that motorists spent on gas

Given:

We find

(a) P[the probability that a motorist spent more than $835 on gas]

From Normal Probability Integral table

The required probability is 0.7422

(b) P[the probability that a motorist spent between $828 and $942 on gas]

(Due to symmetry)

From Normal Probability integral table

The required probability is 0.4270

(c) 75% of motorists spent less than k amount on gas such that,

......................(1)

From Normal Probability Integral table

......................(2)

From equation (1) and (2) we get,

75% of motorists spent less than 967 amount on gas.

(d)  Between two amounts symmetrically distributed about the mean did 70% of motorists spend on gas such that,

...................(1)

From Normal Probability Integral table

......................(2)

From equation (1) and (2) we get,

The amounts symmetrically distributed about the mean did 70% of motorists spend on gas lie between and