Question

In: Statistics and Probability

IQ scores are standardized such that the population of scores has a mean of 100 and...

IQ scores are standardized such that the population of scores has a mean of 100 and a variance of 225. Assuming IQ scores have a normal distribution, what proportion of scores will fall below 80? What proportion will fall below 75?

What values occur in the top 9% of the distribution? What values occur in the bottom 9% of the distribution?

Expert Solution

Suppose, random variable X denotes IQ score.

(a)

Corresponding probability is given by

[Using R-code 'pnorm(-1.333333)']

Hence, 0.09121127 proportion of scores will fall below 80.

(b)

Corresponding probability is given by

[Using R-code 'pnorm(-1.666667)']

Hence, 0.04779032 proportion of scores will fall below 75.

(c)

We have to find so that

[Using R-code 'qnorm(1-0.09)']

Hence, values higher than 120.1113 occur in the top 9% of the distribution.

(d)

We have to find so that

[Using R-code 'qnorm(0.09)']

Hence, values lower than 79.8887 occur in the bottom 9% of the distribution.

orchestra answered 1 year ago

Assuming IQ scores are normally distributed in the population with a mean of 100 and a...

Assuming IQ scores are normally distributed in the population with a mean of 100 and a standard deviation of 16, what percentages of IQ scores are less than 120, between 110 and 130, and what IQ will place you in the top 8% of the population?

IQ scores are known to be normally distributed. The mean IQ score is 100 and the...

IQ scores are known to be normally distributed. The mean IQ score is 100 and the standard deviation is 15. What percent of the population has an IQ between 85 and 105. Need to solve it through Excel

Exam scores for a population were standardized with a population mean (µ) of 500 and a...

Exam scores for a population were standardized with a population mean (µ) of 500 and a population standard deviation (σ) of 100 on both the Math and Verbal portions. The following questions refer to the Math portion; a) A highly selective school decides that it will consider only applicants with a score in the top 5%. What will be the minimum score that you must have in order to be considered for admission to this school? b) If 1 million...

The population of IQ scores form a normal distribution with a μ = 100 and a...

The population of IQ scores form a normal distribution with a μ = 100 and a standard deviation of σ = 10. What is the probability of obtaining a sample mean greater than M = 97, For a random sample of n = 9 For a random sample of n = 25 people

1. The standardized IQ test is described as a normal distribution with 100 as the mean...

1. The standardized IQ test is described as a normal distribution with 100 as the mean score and a 15-point standard deviation. a. What is the Z-score for a score of 150? b. What percentage of scores are above 150? c. What percentage of scores fall between 85 and 150? d. What does it mean to score in the 95th percentile? e. What is the score that corresponds to being in the 95th percentile? 2. A friend wants to learn...

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?

IQ scores in a certain population are normally distributed with a mean of 97 and a...

IQ scores in a certain population are normally distributed with a mean of 97 and a standard deviation of 12. (Give your answers correct to four decimal places.) (a) Find the probability that a randomly selected person will have an IQ score between 92 and 98. (b) Find the probability that a randomly selected person will have an IQ score above 90 .

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...

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...

assume that IQ scores are normally distributed with a mean of 100 and a standard deviation...

assume that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a randomly selected person has an IQ score less than 115. Find the probability that a randomly selected person has an IQ score greater than 118. Find the probability that a randomly selected person has an IQ score between 88 and 112.