MATHEMATICS COLLEGE

According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1,999. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $574. (Round your z-score computation to 2 decimal places and final answers to 2 decimal places.) What percent of the adults spend more than $2,550 per year on reading and entertainment?

Answers

Answer 1

Answer:

Answer:

The probability is $P(X > x ) = 0.19215$

Step-by-step explanation:

From the question we are told that

Th The population mean $\mu = \$ 1,999$

The standard deviation is $\sigma = \$ 574$

The values considered is $x = \$ 2,500$

Given that the distribution of the amounts spent follows the normal distribution then the percent of the adults spend more than $2,550 per year on reading and entertainment is mathematically represented as

$P(X > x ) = P(( X - \mu)/(\sigma ) > ( x - \mu)/(\sigma ) )$

Generally

$X - \mu}{\sigma } = Z (The \ standardized \ value \ of \ X )$

$P(X > x ) = P(Z > ( x - \mu)/(\sigma ) )$

substituting values

$P(X > 2500 ) = P(Z > ( 2500 - 1999)/(574 ) )$

$P(X > 2500 ) = P(Z >0.87 )$

From the normal distribution table the value of $P(Z >0.87 )$ is

$P(Z >0.87 ) = 0.19215$

Thus

$P(X > x ) = 0.19215$

Answer 2

Answer:

Final answer:

We calculate the z-score for the amount $2,550 using the given mean and standard deviation. The z-table gives us the percentage of people who spend less than this, which we subtract from 1 to find the percentage who spend more. Approximately 16.85% of adults in the 25- to 34-year age group spend more than $2,550 on reading and entertainment each year.

Explanation:

To compute the percentage of adults spending more than $2,550 per year, we must first find the z-score associated with this value. The z-score is a measurement of how many standard deviations a particular data point is from the mean.

The formula for calculating the z-score is: Z = (X - μ) / σ.

Where:
- X is the value we are interested in.
- μ is the mean.
- σ is the standard deviation.

Using this formula, the z-score for $2,550 is:
Z = ($2,550 - $1,999) / $574 = 0.96.

Next, we need to use a z-table or a standard normal distribution table to find out the probability that lies below the calculated z-score. Looking this up on a z-table, we get a value of 0.8315, meaning that 83.15% of the population will spend $2,550 or less per year on reading and entertainment. Since we want to know the percentage spending more than $2,550, we subtract this value from 1: 1 - 0.8315 = 0.1685.

Therefore, based on the given mean and standard deviation, about 16.85% of adults in the 25- to 34-year age group spend more than $2,550 on reading and entertainment each year.

Learn more about Z-Score here:

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Find the 1000th term for the sequence

Answers

Answer:

D. 7017

Step-by-step explanation:

if 24 is the first term, find 7x999, or 7x1000-7 and add 24

however a better way would be to use the formula

value=a+(n-1)d

a = the first term in the sequence (24)

n = the amount of terms you need (1000)

d = the common difference between terms (7)

Ty stacked some large wooden blocks. Each block is 1/3 ft tall. His stack of blocks measures 5 ft. How many blocks are in Ty's stack?

Answers

5 / (1/3) = 15

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Consider a disease whose presence can be identified by carrying out a blood test. Let p denote the probability that a randomly selected individual has the disease. Suppose n individuals are independently selected for testing. One way to proceed is to carry out a separate test on each of the n blood samples. A potentially more economical approach, group testing, was introduced during World War II to identify syphilitic men among army inductees. First, take a part of each blood sample, combine these specimens, and carry out a single test. If no one has the disease, the result will be negative, and only the one test is required. If at least one individual is diseased, the test on the combined sample will yield a positive result, in which case the n individual tests are then carried out. [The article "Random Multiple-Access Communication and Group Testing"† applied these ideas to a communication system in which the dichotomy was active/idle user rather than diseased/nondiseased.] If p = 0.15 and n = 5, what is the expected number of tests using this procedure? (Round your answer to three decimal places.)

Answers

Answer:

The expected number of tests, E(X) = 6.00

Step-by-step explanation:

Let us denote the number of tests required by X.

In the case of 5 individuals, the possible value of x are 1, if no one has the disease, and 6, if at least one person has the disease.

To find the probability that no one has the disease, we will consider the fact that the selection is independent. Thus, only one test is necessary.

Case 1: P(X=1) = [P (not infected)]⁵

= (0.15 - 0.1)⁵

P(X=1) = 3.125*10⁻⁷

Case 2: P(X=6) = 1- P(X=1)

= 1 - (1 - 0.1)⁵

P(X=6) = (1 - 3.125*10⁻⁷) = 0.999999

P(X=6) = 1.0

We can then use the previously determined values to compute the expected number of tests.

E(X) = ∑x.P(X=x)

= (1).(3.125*10⁻⁷) + 6.(1.0)

E(X) = E(X) = 6.00

Therefore, the expected number of tests, E(X) = 6.00

Convert 100 inches per minute to feet per hour?

Answers

100 inches per minute
There are 60 minutes per hour so
100 inches per minute equals
6,000 inches per hour
there are 12 inches per foot so that converts to
500 feet per hour

Please help! Thank you!

Answers

The exact values of α and β as follows: α = 2π/3 and β = 7π/6. To find the exact value of the given trigonometric expressions, we need to use the Laws of Sines and Cosines.

What is Law of Sines?

The Law of Sines is a mathematical equation used to calculate the angles or sides of a triangle when two angles and one side are known. It states that the ratio of the sine of an angle to the length of the opposite side is constant.

The Law of Sines states that the ratio of a side to the sine of its opposite angle is equal for all sides and angles of a triangle. The Law of Cosines states that the square of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those sides multiplied by the cosine of the included angle.

We begin by finding the exact value of tan α. Using the Law of Sines, we can find the measure of α by solving the equation: tan α = 3/4 = sin α/cos α. This can be rearranged to find cos α = 4/3, and then we can use the inverse of cosine to find the exact value of α.

Using the Law of Cosines, we can find the exact value of β by solving the equation: -15/17 = (cos β)2 = (1 - sin2 β). This can be rearranged to find sin β = -4/5, and then we can use the inverse of sine to find the exact value of β.

Finally, using the given conditions, we can find the exact values of α and β as follows: α = 2π/3 and β = 7π/6.

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Amanda has been employed at a company for 37 years. The company is 24 years older than Amanda. The sum of Amanda age and the company’s age is 121 years. How old was Amanda when she started her job?