Question

In: Statistics and Probability

IQ scores are scaled to have a mean of 100 and a standard deviation of 15....

IQ scores are scaled to have a mean of 100 and a standard deviation of 15. They are also supposed to follow a normal distribution. Suppose a random sample of 81 people are given IQ tests. Calculate the probability that the sample mean IQ is greater than 102.

Solutions

Expert Solution

Solution :

Given that ,

mean = = 100

standard deviation = = 15

n = 81

= 100

=  / n = 15/ 81=1.6667

P( >102 ) =1 - P( < 102)

=1- P[( - ) / < (102-100) /1.6667 ]

= 1-P(z <1.20 )

Using z table  

= 1- 0.8849   

probability=0.1151

orchestra answered 1 year ago
Next > < Previous

Related Solutions

IQ scores have a mean of 100 and standard deviation of 15: a) What percentage of...
IQ scores have a mean of 100 and standard deviation of 15: a) What percentage of scores fall between 100 & 135? b) What percentage of scores fall between 88 & 100?
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15....
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. A) If one person are randomly selected, find the probability the IQ score is greater than 112. B)If one person are randomly selected, find the probability the IQ score is less than 95. C)If one person are randomly selected, find the probability the IQ score is between 97 and 110. D) If 16 people are randomly selected, find the probability the IQ score will...
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15....
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. a) Find the proportion of the population that has an IQ higher than 94 b) Find the proportion of the population that has an IQ between 82 and 88 c) Find the IQ score that seperates the highest scoring 67% from the rest of the population Critical Values Z0.05= 1.645 Z0.025=1.96 Z0.01=2.325 Z0.005=2.575
IQ Scores are normally distributed with a mean of 100 and a standard deviation of 15....
IQ Scores are normally distributed with a mean of 100 and a standard deviation of 15. Use this information and a Z-table (or calculator or Excel) to solve the following problems. A. Ryan has an IQ score of 118. Calculate the z-score for Ryan's IQ. B. Interpret the z-score you obtained in the previous problem. C. Suppose an individual is selected at random. What is the probability that their IQ score is less than 111? Round your answer to four...
IQ scores in a large population have a normal distribution with mean=100 and standard deviation=15. What...
IQ scores in a large population have a normal distribution with mean=100 and standard deviation=15. What is the probability the sample mean for n=2 will be 121 or higher? (I understand the z score equals 1.98,could you please explain to me how the final answer is equal to 0.0239?thanks.) Also, why do we use 1 and subtract 0.9761 to get 0.0239? Where does 0.9761 come from?
The mean population IQ is 100 with a standard deviation of 15. A principal at a...
The mean population IQ is 100 with a standard deviation of 15. A principal at a certain school claims that the mean IQ score of their students in his school is greater that 100. A random sample of 30 students IQ scores have a mean score of 112. Significance level α = 0.01 (a) State the null and alternate hypotheses (b) Calculate the z statistic value 6 (c) Determine the p value. Sketch the graph (d) Make a decision. Reject...
IQ is normally distributed with a mean of 100 and a standard deviation of 15. a)...
IQ is normally distributed with a mean of 100 and a standard deviation of 15. a) Suppose one individual is randomly chosen. Find the probability that this person has an IQ greater than 95. Write your answer in percent form. Round to the nearest tenth of a percent. P (IQ greater than 95) = % b) Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125. Write your answer in percent form....
IQ is normally distributed with a mean of 100 and a standard deviation of 15. a)...
IQ is normally distributed with a mean of 100 and a standard deviation of 15. a) Suppose one individual is randomly chosen. Find the probability that this person has an IQ greater than 95. Write your answer in percent form. Round to the nearest tenth of a percent. P P (IQ greater than 95) = % b) Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125. Write your answer in percent...
. IQ is normally distributed with a mean of 100 and a standard deviation of 15....
. IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose an individual is randomly chosen. a) (3pt) Find the probability that the person has an IQ greater than 125. b) (4pt) Find the probability that the person has an IQ score between 105 and 118. c) (4pt) What is the IQ score of a person whose percentile rank is at the 75th percentile, ?75? d) (3pt) Use the information from part (c) to...
IQ test scores are normally distributed with a mean of 100 and a standard deviation of...
IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individual's IQ score is found to be 123. A.What percentage of individuals will score above 123? B.What percentage of individuals will score below 123? c. What percentage of individuals will score between 123 and 100? d. This individual was trying to be in the 80th percentile; did they achieve this? how can you tell? e. what can we say about someone with...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT