A company makes a profit of $1.38 million. This is $2.54 million more than last year. Write and solve an equation to find the pr

El cuadro de proporciones debe reflejar dimensiones que sean comparables a las del rectángulo original. Es decir, las medidas de los rectángulos adicionales deben multiplicarse por un factor de escala para hacer el aumento. Revisé cada medida para confirmar si era un múltiplo del rectángulo original.

Answer:

(a) What will his age be after 5 years?

"5 + y" years old

(b) What was his age 6 years ago?

"y - 6" years old

(c) If his grandfather’s age is five times his, how old is his grandfather?

"5y" years old

(d) His father is 6 years older than three times his age. How old is his father?

"6 + 3y" years old

Note: Disregard the quotation marks, ""

Response:

Detailed explanation:

Greetings!

You have the variable

X: Area eligible for painting with a can of spray paint (feet²)

This variable is normally distributed with a mean of μ= 25 feet² and a standard deviation of δ= 3 feet²

As this variable has a normal distribution, it needs to be converted into the standard normal form to utilize tabulated cumulative probabilities.

a.

P(X>27)

The first step involves standardizing the X value using Z= (X-μ)/ δ ~N(0;1)

P(Z>(27-25)/3)

P(Z>0.67)

Having determined the Z value, you can find it in the table, but since the table includes probabilities for , the following conversion must be applied:

P(Z>0.67)= 1 - P(Z≤0.67)= 1 - 0.74857= 0.25143

b.

A sample of 20 cans was taken, and you need to ascertain the probability of averaging a coverage area of 540 feet².

The sample mean maintains the same distribution as its source variable, but its variance is influenced by sample size, thus it is normally distributed with parameters:

X[bar]~N(μ;δ²/n)

To cover 540 feet² with 20 cans, the average coverage must be approximately 540/20= 27 feet² per can.

c.

No, if the distribution is not normal and skewed, the normal distribution should not be applied for calculating probabilities. While the central limit theorem might approximate the sampling distribution to normal when the sample size is 30 or larger, that isn’t applicable here.

I trust this information is helpful!