1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Elden [556K]
2 years ago
11

There are 42 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time

needed to grade a randomly chosen first examination paper is a random variable with an expected value of 5 min and a standard deviation of 6 min. (Give answers accurate to 3 decimal places.)
(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?
1
(b) If the sports report begins at 11:10, what is the probability that he misses part of the report if he waits until grading is done before turning on the TV?
2

Mathematics
1 answer:
harkovskaia [24]2 years ago
5 0

Answer:

A) 0.99413

B) 0.00022

Step-by-step explanation:

A) First of all let's find the total grading time from 6:50 P.M to 11:00 P.M.:

Total grading time; X = 11:00 - 6:50 = 4hours 10minutes = 250 minutes

Now since we are given an expected value of 5 minutes, the mean grading time for the whole population would be:

μ = n*μ_s ample = 42 × 5 = 210 minutes

While the standard deviation for the population would be:

σ = √nσ_sample = √(42 × 6) = 15.8745 minutes

To find the z-score, we will use the formula;

z = (x - μ)/σ

Thus;

z = (250 - 210)/15.8745

z = 2.52

From the z-distribution table attached, we have;

P(Z < 2.52) ≈ 0.99413

B) solving this is almost the same as in A above, the only difference is an additional 10 minutes to the time.

Thus, total time is now 250 + 10 = 260 minutes

Similar to the z-formula in A above, we have;

z = (260 - 210)/15.8745

z = 3.15

P(Z > 3.15) = 0.00022

You might be interested in
The sum of three numbers is 97. The third number is 2 times the second. The second number is 9 less than the first. What are the
inn [45]

Answer:

The numbers are 26.5, 53 and 17.5.

Step-by-step explanation:

97=x+(x-9)+2x

97+9=4x

106/4=4x/4

x= 26.5

x-9 = 17.5

2x= 53

8 0
3 years ago
Simplify<br> 7x + 2y - 3x + 4y<br><br> Factorise<br> 10x - 15<br><br> Solve<br> 5p = 3p + 8
vlada-n [284]

Answer:

1. x = -1.5y

2. 5 (2x-3)

3. p = 4

Step-by-step explanation:

1) Simplifying

7x + 2y + -3x + 4y = 0

Reorder the terms:

7x + -3x + 2y + 4y = 0

Combine like terms: 7x + -3x = 4x

4x + 2y + 4y = 0

Combine like terms: 2y + 4y = 6y

4x + 6y = 0

Solving

4x + 6y = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6y' to each side of the equation.

4x + 6y + -6y = 0 + -6y

Combine like terms: 6y + -6y = 0

4x + 0 = 0 + -6y

4x = 0 + -6y

Remove the zero:

4x = -6y

Divide each side by '4'.

x = -1.5y

Simplifying

x = -1.5y

2)

Common factor

10x - 15

5 (2x-3)

3) Simplifying

5p = 3p + 8

Reorder the terms:

5p = 8 + 3p

Solving

5p = 8 + 3p

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-3p' to each side of the equation.

5p + -3p = 8 + 3p + -3p

Combine like terms: 5p + -3p = 2p

2p = 8 + 3p + -3p

Combine like terms: 3p + -3p = 0

2p = 8 + 0

2p = 8

Divide each side by '2'.

p = 4

Simplifying

p = 4

7 0
2 years ago
297 words in 5.5 minutes ? im confused again
Vedmedyk [2.9K]

Answer:

The unit rate of 297 words for 5.5 minutes is, 54 words per minutes

hope this helps :-)

5 0
2 years ago
Jane is helping the librarian stack books on some new shelves. She is to stack 116 books on 16 shelves. The librarian told her t
goblinko [34]

Answer:

No

Step-by-step explanation:

This is not possible for Jane to put the same amount it all depends on how the book fits, how thick it is, how skinny it is and what else is on the shelf.

4 0
3 years ago
Read 2 more answers
How to simplify the square root of 9/245
lana66690 [7]
<span><span>the exact answer is 3 over
 <span>5√</span> </span>35</span>
8 0
3 years ago
Other questions:
  • Critical points of x+5/x+2&gt;0
    12·1 answer
  • The graph of y = -3+4 is:
    6·1 answer
  • Monica is mixing some custom-colored paint for her house. The color she wants requires 3⁄4 ounce of blue dye and 2⁄3 of an ounce
    7·2 answers
  • 18, 14, 9, 15, 19, 9<br>Mean_<br>Median showing work ​
    10·1 answer
  • Does this horizontal line have a slope? Explain pls.
    10·1 answer
  • If a1=10 and an=an-1+4 then find the value of a5
    13·1 answer
  • Triangle DAN has coordinates D(-10,4), A(-4,1), and N(-2,5) Using coordinate geometry, prove that triangle DAN is a right triang
    14·1 answer
  • Find the perimeter. Simplify your answer.<br> 3x+7<br> 3x+7<br> 2x-3
    7·1 answer
  • Read the screenshot thanks
    6·1 answer
  • Lucy Garcia took out a loan for $40,000 at 10 percent interest for 10 years. Her monthly payments are $528. 60. She made payment
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!