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
Marianna [84]
3 years ago
14

Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering

a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi is a good student for whom p = 0.85.(a) Use the normal approximation to find the probability that Jodi scores 78% or lower on a 100-question test.(b) If the test contains 250 questions, what is the probability that Jodi will score 78% or lower?
Mathematics
1 answer:
Alla [95]3 years ago
6 0

Answer:

a) The probability that Jodi scores 78% or lower on a 100-question test is 4%.

b) The probability that Jodi scores 78% or lower on a 250-question test is 0.023%.

Step-by-step explanation:

a) To approximate this distribution we have to calculate the mean and the standard distribution.

The mean is the proportion p=0.85.

The standard deviation can be calculates as:

\sigma=\sqrt{\frac{p(1-p)}{n} }= \sqrt{\frac{0.85*(1-0.85)}{100} }=0.04

To calculate the probability that Jodi scores 78% or less on a 100-question test, we first calculate the z-value:

z=\frac{p-p_0}{\sigma} =\frac{0.78-0.85}{0.04} =-1.75

The probability for this value of z is

P(x

The probability that Jodi scores 78% or lower on a 100-question test is 4%.

b) In this case, the number of questions is 250, so the standard deviation needs to be calculated again:

\sigma=\sqrt{\frac{p(1-p)}{n} }= \sqrt{\frac{0.85*(1-0.85)}{250} }=0.02

To calculate the probability that Jodi scores 78% or less on a 250-question test, we first calculate the z-value:

z=\frac{p-p_0}{\sigma} =\frac{0.78-0.85}{0.02} =-3.5

The probability for this value of z is

P(x

The probability that Jodi scores 78% or lower on a 250-question test is 0.023%.

You might be interested in
What would your salary each year be if you earned $5,000 per week?
choli [55]
Yearly salary would be 240,000 for 5,000 and 48,000 for 1,000 a week
8 0
3 years ago
X = ? y = ? 16 45 degrees
mezya [45]

Let's put more details in the figure to better understand the problem:

Let's first recall the three main trigonometric functions:

\text{ Sine }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Hypotenuse}}\text{ Cosine }\theta\text{ = }\frac{\text{ Adjacent Side}}{\text{ Hypotenuse}}\text{ Tangent }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Adjacent Side}}

For x, we will be using the Cosine Function:

\text{ Cosine }\theta\text{ = }\frac{\text{ Adjacent Side}}{\text{ Hypotenuse}}Cosine(45^{\circ})\text{ = }\frac{\text{ x}}{\text{ 1}6}(16)Cosine(45^{\circ})\text{ =  x}(16)(\frac{1}{\sqrt[]{2}})\text{ = x}\text{ }\frac{16}{\sqrt[]{2}}\text{ x }\frac{\sqrt[]{2}}{\sqrt[]{2}}\text{ = }\frac{16\sqrt[]{2}}{2}\text{ 8}\sqrt[]{2}\text{ = x}

Therefore, x = 8√2.

For y, we will be using the Sine Function.

\text{  Sine }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Hypotenuse}}\text{ Sine }(45^{\circ})\text{ = }\frac{\text{ y}}{\text{ 1}6}\text{ (16)Sine }(45^{\circ})\text{ =  y}\text{ (16)(}\frac{1}{\sqrt[]{2}})\text{ = y}\text{ }\frac{16}{\sqrt[]{2}}\text{ x }\frac{\sqrt[]{2}}{\sqrt[]{2}}\text{ = }\frac{16\sqrt[]{2}}{2}\text{ 8}\sqrt[]{2}\text{ = y}

Therefore, y = 8√2.

5 0
1 year ago
Please tell me what is (7+3x)4
Savatey [412]

Answer:

28+12x

Step-by-step explanation:

Multiply 7 with 4

Multiply 3x with 4

5 0
2 years ago
Read 2 more answers
Hello dear students.
Vladimir [108]
Theater means expressing your own emotions and feelings in your own way without anyone judging you, express and grow your talent everyday with people who want to succeed in the same as you. Theater always has a story behind every sentence, poem, show, actor, etc…
7 0
2 years ago
hey can you help me w/ some math ?? i make $8.50 an hour. monday through sunday only wednesday’s off. how much will i have in 2
enot [183]

Answer:

$29252.1669

Approximately $29252.1

Step-by-step explanation:

For Monday,  Tuesday and Sunday:

=> 8.50 x 5 x 3

=> 8.5 x 15

=> 127.5

I multiplied 8.5 and 5 because you work for 5 hours. Then multiplied them with 3 it is for 3 days.

For Friday, Saturday, Thursday:

=> 8.5 x 6 x 3

=> 8.5 x 18

=> 153

I multiplied 8.5 and 6 because you work for 6 hours. Then multiplied them with 3 because it is for 3 days.

In 1 week you get:

=> 153 + 127.5

=> 280.5

In 1 year there are 52.1429 weeks.

So, you get:

=> 52.1429 x 280.5

=> 14626.08345

For 2 years, you get:

=> 14626.08345x 2

=>  29252.1669

=> Approximately $29252.1

8 0
3 years ago
Other questions:
  • Anyone know how to answer this? Help if u do please!
    11·2 answers
  • Kypton finished 3/8 of his homework. Paxton finished 6/8 of his homework. How much more homework did Paxton do than Kypton?
    6·1 answer
  • A system of equations has no solution. If y = 8x + 7 is one of the equations, which could be the other equation?
    14·1 answer
  • $2,200 people enter an amusement park every hour. How long will it take for 6,600 people to enter the park ?
    9·2 answers
  • A large bowl contains 10 small balls and each ball has a color and a number. The 10 balls are denoted by B1, B2, B3, B4, R1, R2,
    7·1 answer
  • Is x^2+y^2=5 a function? why or why not?
    12·1 answer
  • if 24000 bricks of the same shape and size are required to build a wall of dimensions 15m*6m*20cm ,find the volume of each brick
    14·1 answer
  • (12x+5)°=(17x-5)°<br> Find x=?
    11·1 answer
  • Adrian, Ben and Charlie share some sweets in the ratio 6:3:8
    6·1 answer
  • Which ordered pair is a solution to the system of linear equation? 2x+ 3y=6 <br> -3x+5y=10
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!