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
elena55 [62]
3 years ago
11

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​?
Mathematics
1 answer:
Yuri [45]3 years ago
5 0

Answer:

(a) 68% of people has an IQ score between 87 and 113​.

(b) 5% of people has an IQ score less than 74 or greater than 126.

(c) 0.15% of people has an IQ score greater than 139​.

Step-by-step explanation:

Given information:Scores of an IQ test have a​ bell-shaped distribution,

mean = 100

standard deviation = 13

According to the empirical rule

68% data lies between \overline{x}-\sigma and \overline{x}+\sigma.

95% data lies between \overline{x}-2\sigma and \overline{x}+2\sigma.

99.7% data lies between \overline{x}-3\sigma and \overline{x}+3\sigma.

(a)

\overline{x}-\sigma=100-13=87

\overline{x}+\sigma=100+13=113

[\overline{x}-\sigma,\overline{x}+\sigma]=[87,113]

Using empirical rule we can say that 68% of people has an IQ score between 87 and 113​.

(b)

\overline{x}-2\sigma=100-2(13)=74

\overline{x}+2\sigma=100+2(13)=126

[\overline{x}-2\sigma,\overline{x}+2\sigma]=[74,126]

Using empirical rule we can say that 95% of people has an IQ score between 74 and 126​.

The percentage of people has an IQ score less than 74 or greater than 126 is

P = 1- percent of people has an IQ score between 74 and 126​.

P = 1- 95%

P = 5%

Therefore 5% of people has an IQ score less than 74 or greater than 126.

(c)

\overline{x}-3\sigma=100-3(13)=61

\overline{x}+3\sigma=100+3(13)=139

[\overline{x}-3\sigma,\overline{x}+3\sigma]=[61,139]

Using empirical rule we can say that 99.7% of people has an IQ score between 61 and 139​.

The percentage of people has an IQ score less than 61 or greater than 139 is

P = 1- percent of people has an IQ score between 61 and 139​.

P = 1- 99.7%

P = 0.3%

The percentage of people has an IQ score greater than 139​ is

P=\frac{1}{2}(0.3\%)=0.15\%

Therefore 0.15% of people has an IQ score greater than 139​.

You might be interested in
Why is -10+(-10)=0 wrong
kenny6666 [7]

Step-by-step explanation:

because because that would be subtracting positive 10 by -10. not adding -10 + -10 which would be 20

5 0
3 years ago
Read 2 more answers
13. Find the equations of the straight lines which passes
ipn [44]

9514 1404 393

Answer:

  • y = 1/2x +2
  • y = -2x +7

Step-by-step explanation:

The slope of a line is the tangent of the angle it makes with the x-axis. The given line has a slope of -1/3, so the lines we want will have slopes of ...

  m1 = tan(arctan(-1/3) +45°) = 0.5 . . . . . using a calculator

  m2 = tan(arctan(-1/3) -45°) = -2

Of course, these two lines are perpendicular to each other, so their slopes will have a product of -1: (0.5)(-2) = -1.

__

We can use the point-slope form of the equation for a line to write the desired equations:

  y = m(x -h) +k . . . . . line with slope m through point (h, k)

<u>Line 1</u>:

  y = 1/2(x -2) +3

  y = 1/2x +2

<u>Line 2</u>:

  y = -2(x -2) +3

  y = -2x +7

3 0
3 years ago
Sarah has gone four weeks. Micah has been recording the daily high temperature. During that time, the high temperature has been
pickupchik [31]
The experimental probability that the high temp will be below 45 F on the 29th day is, 4.5 out of 29 days, that is because 20 of the days have had lower temperatures, so they left 9 days of and from those 9 days, they could be lower or greater that 45F (50% each side), that is:
4.5/29 = 0.155 = 15.5%
that is the exp probability
8 0
3 years ago
What multiplication equation can you use to check the answer to the problem -32 divided by -4
Naddika [18.5K]

8x-4=-32 so thats an equation that you can use

5 0
3 years ago
Angles A and B are supplementary.Angle A has a measure of 80 degrees. What is the measure of angle B
yulyashka [42]

The sum of two supplementary angles is 180 degrees.

A+B=180.

80+B=180

B= 180-80

B=100

8 0
3 years ago
Read 2 more answers
Other questions:
  • Which shows the equation of the line using function notation?
    10·1 answer
  • A paint store has 35 gallons of paint in storage, 2/5 are for outdoor use. if each gallon cost $22, what is the total cost of th
    5·1 answer
  • Jan noticed at the store that a sweater costs $3.95 more than a shirt. she bought 3 shirts and 2  sweaters and the total costs (
    9·1 answer
  • How do u graph 3/4 x+2
    5·2 answers
  • During halftime of a football game, a slingshot launcher’s T-shirts at the crowd. A T-shirt is launch from a height of 3 feet wi
    5·1 answer
  • 20 pts to whoever helps!!
    7·1 answer
  • Fran bought 4 shirts that were each $13 each. She also bought a pair of socks for 4.29. What was the total amount Fran pair for
    11·1 answer
  • Apples are on sale at four different grocery stores. Which store offers the
    9·1 answer
  • 1. Camille received $1000 in graduation gifts. He found a savings plan that will pay him 4% interest compounded continuously. Us
    6·1 answer
  • Small tug boats pull cruise ships up and down rivers to prevent them from grounding. Cruise ships anchor 22 km away from the riv
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!