Question

Suppose that daycare costs are normally distributed with a mean equal to $10,000 a year and a standard deviation equal to $2,000.

what percentage of daycare cost over $10,000?
what percentage of daycare cost between $8,000 and $12,000?
what percentage of daycare cost between $6,000 and $14,000?

Answer 1

50%, 68.26%, 95.54%

Explanation:

Let X be the day care costs

X is N(10000, 2000)

Since normal distribution is symmetrical about the mean we get

above 10000, exactly 50% of day care cost would be .

Between 8000 and 12000,

=
`P(8000<x<12000)*100\\=P(|x-\mu|<2000)*100\\= P(|z|<1) *100\\= 68.26%`

Between 6000 and 14000

`P(6000<x<14000)\\= P(|x-\mu|<4000)\\= P(|Z|<2)\\= 200(0.4772)\\= 95.54`%