A machine fills boxes at a constant rate. At the end of 35 minutes, it has filled 5 boxes.

The average high-school teacher annual salary is $43,000. Let teacher salary be normally distributed with a standard deviation o

Dvinal [7]

Answer:

a) 0.219

b) 0.02

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 43000, \sigma = 18000$

a. What percent of high school teachers make between $40,000 and $50,000?

This is the pvalue of Z when X = 50,000 subtracted by the pvalue of Z when X = 40,000.

So

X = 50,000

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{50000 - 43000}{18000}$

$Z = 0.39$

$Z = 0.39$ has a pvalue of 0.6517.

X = 40,000

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{40000 - 43000}{18000}$

$Z = -0.17$

$Z = -0.17$ has a pvalue of 0.4325

So 0.6517 - 0.4325 = 0.219 = 21.9% of high school teachers make between $40,000 and $50,000.

b. What percent of high school teachers make more than $80,000?

This is 1 subtracted by the pvalue of Z when X = 80000. SO

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{80000 - 43000}{18000}$

$Z = 2.06$

$Z = 2.06$ has a pvalue of 0.9803.

So 1-0.9803 = 0.0197 = 0.02 = 2% of high school teachers make more than $80,000.

6 0

3 years ago

James wants to send two gifts by mail. One package weighs 2 3/4 pounds. The other package weighs 1 3/4. Want is the total weight

LUCKY_DIMON [66]

= 4 1/2 (2 3/4 + 1 3/4)

Hope you give the brainliest answer.

8 0

3 years ago

Simplify the expression under the square root sign

liraira [26]

Answer:

Reaction time tests can be used to assess an individual's hand-eye coordination. One test involves catching a 1 metre ruler and measuring the distance, d in metres, that the ruler travelled before being caught. The reaction time t seconds is then calculated using the formula: = √2d/9.8

3 0

3 years ago

PLEASE HELP ASAP

Mice21 [21]

Answer:

2,100 people

Step-by-step explanation:

~Divide to find the number of people in fifths

3,500 / 5 = 700

~Multiply to find 2/5 of the total people

700 * 2 = 1,400

~Subtract to find the number of people against building the school.

3,500 - 1,400 = 2,100

Best of Luck!

3 0

3 years ago

Write the point-slope form of the line that passes through (6, 1) and is parallel to a line with a slope of -3. Include all of y

denpristay [2]

Answer:

$(y - 1) = -3(x - 6)$

Step-by-step explanation:

The equation of a line in point-slope form is

$(y-y_{1}) = m (x-x_{1})$

where y1 and x1 are 2 known points, and m is the slope of the line. So simply just fill in the blanks.

y is a variable so it is left alone (since there is no subscript).

y1 we are told is 1.

m we are told is -3 (the slope)

x is a variable so it is left alone (since there is no subscript).

x1 we are told is 6.

3 0

3 years ago