# Mathematics achievement test scores for 300 students were found to have a mean and a variance equal to 600 and 3600, respectively. (a) If the distribution of test scores was mound-shaped, approximately how many of the scores would fall into the interval 540 to 660? (Round your answer to the nearest whole number.) (b) Approximately how many scores would be expected to fall into the interval 480 to 720? (Round your answer to the nearest whole number.)

(a) Approximately 205 students scored between 540 and 660.

(b) Approximately 287 students scored between 480 and 720.

Step-by-step explanation:

A mound-shaped distribution is a normal distribution since the shape of a normal curve is mound-shaped.

Let X = test score of a student.

It is provided that .

(a)

The probability of scores between 540 and 660 as follows:

Use the standard normal table for the probabilities.

The number of students who scored between 540 and 660 is:

300 × 0.6826 = 204.78 ≈ 205

Thus, approximately 205 students scored between 540 and 660.

(b)

The probability of scores between 480 and 720 as follows:

Use the standard normal table for the probabilities.

The number of students who scored between 480 and 720 is:

300 × 0.9544 = 286.32 ≈ 287

Thus, approximately 287 students scored between 480 and 720.

## Related Questions

Streaming movies from Company A costs \$3 per movie plus a monthly fee of \$9. Streaming movies from Company B costs \$4 per movie with no monthly fee. The monthly cost to stream movies depends on the number of movies, m streamed. Which inequality represents the situation when the monthly cost at Company A is less than the monthly cost at Company B?

Answer: 9 + 3 m < 0 + 4 m  or  9 < m

Step-by-step explanation:

Here m represents the number of movies at which the monthly cost of the company A is less than that of company B.

For company A, The monthly cost = \$ 9

And, cost per movie = \$ 3 ⇒ Cost of m movies = 3 m

Therefore, total cost in company A for m movies = 9 + 3 m

Now, For company B, The monthly cost = \$ 0

And, cost per movie = \$ 4 ⇒ Cost of m movies = 4 m

Therefore, total cost in company B for m movies = 0 + 4 m

Thus, 9 + 3 m < 0 + 4 m

⇒ 9 < 4 m - 3 m

⇒ 9 < m

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y + z = 12.

First find a parameterization for the curve of intersection.

Given the equation of a cylinder, a natural choice for a parameterization would be one utilizing cylindrical coordinates. Here,

which suggests we could use

with , and we get from the equation of the plane,

Now use the arc length formula:

What is 2 to the power of 3 over 2 equal to? (5 points) squre root of 8 cube root of 8 cube root of 16 square root of 16

Square root of 8.

Step-by-step explanation:

Given:

Number given : 2 to the power of 3 over 2 equal ...

Using the laws of exponent:

We know that:

⇒  and

So,

According to the question:

2 to the power of 3 over 2  =

Using fractional exponent concept where :

This can be re-written as:

⇒ and that is equivalent to    as  ...

Square root of 8 is our final answer.

A set of books that are each 1.5 inches wide are being organized on a bookshelf that is 36 inches wide. How many books can fit on the shelf?

24 books.

Step-by-step explanation:

The number of books that that can be fitted into the shelf is equal to the width of the self divided by the width of each book:

Step-by-step explanation: To find the answe you would do 36 divides by 1.5 and get 24.

Use traditional algorithm to find the quotient 3 ) 137

Multiply 137 by 3 to get an answer of 411

so far this season Malia scored two goals and missed on her six other shots on goal what is the experimental probability that maria will score a goal on her next shot

Therefore the probability of Maria scoring on her next shot is .

Step-by-step explanation:

i) Maria scored two goals and missed on her other six shots.

ii) Maria took a total of eight shots on the goal.

iii) On an average Maria scored twice in every eight shots or once in every four shots on the goal. So we can say that the probability of Maria scoring a goal on every shot on goal is one in four or .

iv) Therefore the probability of Maria scoring on her next shot is .

Manila walked 4 miles an hour and arrived home in 30 minutes. Her sister ran 6 miles an hour, how long did it take for her to get home.

20 minutes

Step-by-step explanation:

Manila walked home in 30 minutes. She walks 4 miles an hour. Since 30 minutes is half an hour then its half the distance of the rate. 4/2 = 2 miles. This means home is 2 miles away.

Since her sister runs 6 miles an hour, the time it took her will be for only 2 miles. So 6 miles divided into 3 is 2. An hour divided by 3 = 20 minutes. This means her sister travels home 2 miles in 20 minutes.

Ken watches a marching band. He sees 2 rows of flute players. Six people are in each row . He sees 8 trombone players. How many flute players and trombone players does Ken see?

The number of flute players is determined by multiplying the number of rows and the number of people in each row. This is as shown below.
n = (2 rows)(6 people/row) = 12 people (flute players)

The total number of flute players and trombone players can be calculated as shown below,
T = 12 (flute players) + 8 (trombone players)
T = 20 people