the width of a rectangle is 4 less than half the length. if l represents the length, wich equation could be used to find the wid

Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately norm

iragen [17]

Answer:

a. 0.691

b. 0.382

c. 0.933

d. $88.490

e. $58.168

f. 5th percentile: $42.103

95th percentile: $107.897

Step-by-step explanation:

We have, for the purchase amounts by customers, a normal distribution with mean $75 and standard deviation of $20.

a. This can be calculated using the z-score:

$z=\dfrac{X-\mu}{\sigma}=\dfrac{85-75}{20}=\dfrac{10}{20}=0.5\\\\\\P(X$

The probability that a randomly selected customer spends less than $85 at this store is 0.691.

b. We have to calculate the z-scores for both values:

$z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{65-75}{20}=\dfrac{-10}{20}=-0.5\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{85-75}{20}=\dfrac{10}{20}=0.5\\\\\\\\P(65$

The probability that a randomly selected customer spends between $65 and $85 at this store is 0.382.

c. We recalculate the z-score for X=45.

$z=\dfrac{X-\mu}{\sigma}=\dfrac{45-75}{20}=\dfrac{-30}{20}=-1.5\\\\\\P(X>45)=P(z>-1.5)=0.933$

The probability that a randomly selected customer spends more than $45 at this store is 0.933.

d. In this case, first we have to calculate the z-score that satisfies P(z<z*)=0.75, and then calculate the X* that corresponds to that z-score z*.

Looking in a standard normal distribution table, we have that:

$P(z$

Then, we can calculate X as:

$X^*=\mu+z^*\cdot\sigma=75+0.67449\cdot 20=75+13.4898=88.490$

75% of the customers will not spend more than $88.49.

e. In this case, first we have to calculate the z-score that satisfies P(z>z*)=0.8, and then calculate the X* that corresponds to that z-score z*.

Looking in a standard normal distribution table, we have that:

$P(z>-0.84162)=0.80$

Then, we can calculate X as:

$X^*=\mu+z^*\cdot\sigma=75+(-0.84162)\cdot 20=75-16.8324=58.168$

80% of the customers will spend more than $58.17.

f. We have to calculate the two points that are equidistant from the mean such that 90% of all customer purchases are between these values.

In terms of the z-score, we can express this as:

$P(|z|$

The value for z* is ±1.64485.

We can now calculate the values for X as:

$X_1=\mu+z_1\cdot\sigma=75+(-1.64485)\cdot 20=75-32.897=42.103\\\\\\X_2=\mu+z_2\cdot\sigma=75+1.64485\cdot 20=75+32.897=107.897$

5th percentile: $42.103

95th percentile: $107.897

5 0

3 years ago

which description best describes the solution to the following system of equations y= -2x +3 y= -x + 1

marin [14]

For this case we have the following system of equations:
$y = -2x +3

y = -x + 1$
Equating the values of y we have:
$-2x +3 = -x + 1
$
From here, we can clear the value of x.
We have then:
$-2x + x = 1 - 3

-x = -2

x = 2$
Then, we look for the value of y.
For this, we substitute x in any of the equations:
$y = -x + 1

y = -2 + 1

y = -1$
Answer:
The ordered pair solution of the system of equations, is given by:
$(x, y) = (2, -1)$