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
Studentka2010 [4]
3 years ago
13

Scores of an IQ test have a​ bell-shaped distribution with a mean of and a standard deviation of . Use the empirical rule to det

ermine the following. ​(a) What percentage of people has an IQ score between and ​? ​(b) What percentage of people has an IQ score less than or greater than ​? ​(c) What percentage of people has an IQ score greater than ​?
Mathematics
1 answer:
Oduvanchick [21]3 years ago
5 0

Complete question is;

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 13. Use the empirical rule to determine the following.

​(a) What percentage of people has an IQ score between 87 and 113​?

​(b) What percentage of people has an IQ score less than 74 or greater than 126​? ​

(c) What percentage of people has an IQ score greater than 139​?

Answer:

A) 68% of the people had an IQ score between 87 and 113

B) 5% of the people had IQ scores less than 74 and greater than 126.

C) 0.15% had an IQ score greater than 139

Step-by-step explanation:

We are given;

Mean; x¯ = 100

Standard deviation; σ = 13

According to the empirical rule in statistics;

>> 68% of the data lies within one standard deviation of the mean

>> 95% of the data lies within two standard deviations of the mean

>> 99.7% of the data lies within three standard deviations

A) We want to find the percentage of people with an IQ score between 87 and 113.

Within one standard deviation, we have;

x¯ ± σ

>> (100 - 13), (100 + 13)

>> (87, 113) which is the range we are looking for.

Thus, 68% of the people had an IQ score between 87 and 113

B) we want to find percentage of people has an IQ score less than 74 or greater than 126.

Let's first find those who had between 74 and 126.

Let's use two standard deviations within the mean.

x¯ ± 2σ

>> (100 - (2×13)), (100 + (2×13))

>> (74, 126) which is the range we are looking for.

So percentage that have IQ scores between 74 and 126 is 95%

Thus;

Percentage of those who had less than 74 and greater than 126 is;

P = 1 - 95%

P = 5%

C) we want to find the percentage of people that had an IQ score greater than 139.

Let's use the z-score formula;

z = (x¯ - μ)/σ

z = (139 - 100)/13

z = 39/13

z = 3

This means it is 3 standard deviations above the mean.

Thus;

Since it's one side outside the mean, then;

Percentage of people with an IQ score greater than 139 = (1 - 99.7%)/2 = 0.3%/2 = 0.15%

You might be interested in
What is the volume of this right prism?<br><br> 96 in³<br><br> 60 in³<br><br> 48 in³<br><br> 44 in³
yulyashka [42]

Answer:

96 in³

Step-by-step explanation:

Volume = 2(BHD) / 2

The 2s cancel out

Volume = 3(8)4

Volume = 96

4 0
2 years ago
There are 26 third graders and 32 fourth graders going on a field trip. each van carry 10 students. how many students are needed
Zolol [24]
26+32=58
6*10=60
6 vans are needed.
10 students will be in the each of the five vans. 8 students will be in the other van.
6 0
3 years ago
Read 2 more answers
The amount of time it takes Ariana to do a math problem is continuous and uniformly distributed between 38 seconds and 79 second
solniwko [45]

Answer:

29.27% probability that it takes Ariana between 58 and 70 seconds to do a math problem

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X between c and d, d being greater than c, is given by the following formula:

P(c \leq X \leq d) = \frac{d-c}{b-a}

Uniformly distributed between 38 seconds and 79 seconds.

This means that a = 38, b = 79

What is the probability that it takes Ariana between 58 and 70 seconds to do a math problem

c = 58, d = 70

P(58 \leq X \leq 70) = \frac{70 - 58}{79 - 38} = 0.2927

29.27% probability that it takes Ariana between 58 and 70 seconds to do a math problem

4 0
3 years ago
!!!!!Please help !!!!!!
sveta [45]

Answer:

<h2>Cube</h2>

Step-by-step explanation:

<h3>:))))))))))))))))))))</h3>

5 0
3 years ago
Read 2 more answers
You reflect the point ( -7, -6) across
Leokris [45]
Reflecting is pushing it across from one side to another.
The answer would be (7,6)
Sorry I'm late.
4 0
3 years ago
Other questions:
  • Meredith practices the piano for 3 hours each week. How many hours will she practice in 8 weeks?
    13·2 answers
  • Trevor pet goat weighed 6 3/8 pounds when it was born. By age 3, the goat weighed 8 times as much. Fill each box with a number o
    6·1 answer
  • Which of the following relations is a function?
    15·1 answer
  • Solve the following<br> a) 2(x+3)= x-4<br> b) 4(5x-2)= 2(9x+3)
    6·1 answer
  • The International Average Salary Income Database provides a comparison of average salaries for various professions. The data are
    11·1 answer
  • A month of the year is selected at random. What is the probability that it has 31 days or starts with the letter J
    12·1 answer
  • The perimeter of a square is 75inches. What is the length of one side of the square?​
    11·2 answers
  • Like terms 4x + 2x + 7x
    11·2 answers
  • Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.5
    8·2 answers
  • Picture is included ! help please !!
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!