Solve. High school pre-cal

The distribution of income tax refunds follow an approximate normal distribution with a mean of $7010 and a standard deviation o

Andrej [43]

Answer:

A refund must be above $7,139 before it is audited.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 7010, standard deviation = 43.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

The empirical rule is symmetric, which means that the lowest (100-99.7)/2 = 0.15% is at least 3 standard deviations below the mean, and the upper 0.15% is at least 3 standard deviations above the mean.

Use the Empirical Rule to determine approximately above what dollar value must a refund be before it is audited.

3 standard deviations above the mean, so:

7010 + 3*43 = 7139.

A refund must be above $7,139 before it is audited.

5 0

3 years ago

Amy is at the store to buy shorts and pants. the shirts cost $40 each and the pants cost $50 each. she plans to spend no more th

marissa [1.9K]

Answer:

(a) Amy can buy 5 shirts and 4

(b) The combination is correct because it satisfies both inequalities

(c) The two possible ways to show that she can buy is 5 shirt and 4 pants are;

(1) Mathematically

(2) Graphically

Step-by-step explanation:

The given parameters are

The cost of each shirt = $40

The cost of each pant = $50

The amount Amy plans to spend ≤ $400

Let x represent the number of shirts Amy buys and let y represent the number of pants she buys, therefore, we have;

40 × x + 50 × y ≤ 400...(1)

x + y ≥ 5...(2)

Making y the subject of both inequalities gives;

For the inequality (1), we have;

40 × x + 50 × y ≤ 400

y ≤ (400/50) - (40/50) × x = 8 - (4/5)·x

y ≤ 8 - (4/5)·x

For the inequality (2), we have;

x + y ≥ 5

y ≥ 5 - x

Plotting both inequalities using the chart function in Microsoft Excel gives;

(a) As seen from the graph of the system of inequalities, Amy can buy 5 shirts and 4

(b) The combination of 5 shirts and 4 pants as a solution is correct because the value of the total number of the combination is larger than 5 (5 + 4 = 9 > 5) and the cost of 5 shirts plus 4 pants = $400

(c) The two possible ways to show that the combination of shirts and pants that Amy can buy is 5 shirt and 4 pants is a possible solution are;

(1) Mathematically, x = 5, y = 4

Therefore, y ≤ 8 - (4/5) × x gives;

4 ≤ 8 - (4/5) × 5 which is correct and

From y ≥ 5 - x gives;

4 ≥ 5 - 5 = 0, Which is also correct

(2) By plotting a graph of the system of inequalities as included

4 0

3 years ago

Read 2 more answers

The American Community Survey showed that residents of New York City have the longest travel times to get to work compared to re

LiRa [457]

Answer:

The probability it will take a resident of the city between 17.24 and 42.13 minutes to travel to work is 0.3046.

Step-by-step explanation:

The random variable X can be defined as the travel times to get to work.

The expected travel time is, μ = 38.3 minutes.

The distribution of random variable X can be defined as the distribution of time interval between which a person reaches their work place at a constant average rate.

This implies that X follows an Exponential distribution with parameter, $\lambda=\frac{1}{\mu}=\frac{1}{38.3}$ .