Question
Asked Jan 16, 2020
909 views

Scores of An IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 12. Use the empirical rule to determine the following.

a) What percentage of people has an IQ score between 88 and 112?

b) what percentage of people has an IQ score less than 76 or greater than 124?

c) what percentage of people has an IQ score greater than 134?

check_circle

Expert Answer

Step 1

Empirical Rule for normal distribution:

 

  • The percentage of values lies between one standard deviation from the mean is 68%.
  • The percentage of values lies between two standard deviation from the mean is 95%.
  • The percentage of values lies between one standard deviation from the mean is 99.7%
Statistics homework question answer, step 1, image 1
fullscreen
Step 2

 

a)

 

The percentage of people has an IQ score between 88 and 112 is 68% and it is obtained below:

 

From the given information, the scores of an IQ test have a bell-shaped distribution with mean of 100 and a standard deviation of 12.

 

Statistics homework question answer, step 2, image 1
fullscreen
Step 3

That is, the given two values representing the one standard deviation from the mean.

Hence, the percentage of people has an IQ score between 88 and 112 is 68%.

 

b)

 

...
Statistics homework question answer, step 3, image 1
fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Flights According to the Bureau of Transportation, 80.3% of American Airlines flights arrive on time...

A: Solution: We are given that:According to the Bureau of Transportation, 80.3% of American Airlines fl...

question_answer

Q: Powerball As of this writing, the Powerball lottery is run in 44 states. Winning the jackpot require...

A: In Powerball lottery, the winning of jackpot is done by selecting five different correct numbers bet...

question_answer

Q: Rain As the author is creating this exercise, a weather reporter stated that there is a 20% chance o...

A: Let event A denote the chances of rain tomorrow.The probability of chances of rain tomorrow is 20%, ...

question_answer

Q: Answer true or false to the following statement and justify your answer: If event A and event B are ...

A: The statement is “If event A and B are not mutually exclusive, neither are events A, B, and C for ev...

question_answer

Q: The lifetime of a certain brand of battery is normally distributed with a mean value of 8 hr and a s...

A: a.Calculating the probability that the player functions for at least 6 hr:It is given that the lifet...

question_answer

Q: In Exercises 1–5, assume that 74% of randomly selected adults have a credit card (based on results f...

A: Mean is given by:

question_answer

Q: What does it mean for three events to be mutually exclusive?

A: In this case, we need to find the meaning of the statement three events are mutually exclusive.

question_answer

Q: Each of four siblings (Anita, Tony, Maria, and Jose) is given $5,000 to invest in the stock market. ...

A: Given info:The four siblings are Anita, Tony, Maria, and Jose.The four stocks are utility, automotiv...

question_answer

Q: Ethics There are data showing that smoking is detrimental to good health. Given that people could be...

A: It is known that the smoking is bad for health. It is assumed that lives can be saved by decreasing ...