The results of the nationwide aptitude test in Mathematics are normally distributed with mean = 80, and standard deviation=15. What is the percentile rank of the score 84?

Q: A student has taken a 50-point exam and wants to know how his score of 38 compares to the scores of…

A: It is given that Mean = 40 Standard deviation SD = 4 Score X = 38

Q: Georgia is taking a course in statistics (course A) and a course in criminal justice (course B). At…

A: It is required to find the z-scores for the points obtained in the statistics and criminal justice…

Q: A researcher measures the amount of food consumed by each dog in her lab. She finds that the mean…

A: It is given that mean amount of food is 12 oz and number of dogs is 16. The sum of squared…

Q: Scores for a standardized test are normally distributed with a mean of 1200 and a standard…

A: given data μ = 1200σ = 60 normal distributionn = 64P(1200<x¯<1214) = ?

Q: College students average 7.8 hours of sleep per night with a standard deviation of 40 minutes. If…

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Q: The results of a common standardized test used in psychology research is designed so that the…

A:

Q: An IQ exam has a mean of 110 and a standard deviation of 12. What percent of people have an IQ score…

A: Given mean= 110 Standard deviation=12 We know that Z=X-mean/standard deviation

Q: Karen is in her first semester at a certain university and is taking a calculus course with a large…

A: The objective of this question is to calculate the z-score of Karen's exam score and interpret it in…

Q: College students average 7.4 hours of sleep per night with a standard deviation of 45 minutes. If…

A: Given data  college students average 7.4 hrs of sleep with standard deviation of 45mins

Q: A successful basketball player has a height of 6 feet 8 ​inches, or 203 cm. Based on statistics from…

A: Consider X is a random variable defined as the height of a successful basketball player.The provided…

Q: how do you calculate the mean and standard deviation without a calculator ?

A: In this question we have to tell that how to find the Mean and Standard deviation without using the…

Q: The results of a common standardized test used in psychology research is designed so that the…

A: It is given that the mean and standard deviation are 145 and 30.

Q: The average score on the Stats midterm was 70 points with a standard deviation of 6 points,…

A: Given that.   X~N( μ , ?)   μ=70    , ?=6  , Z-score = -1   Z-score =( x - μ )/?

Q: Scores on a test are normally distributed with a mean of 123 and a standard deviation of 20. What…

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Q: cognitive psychologist has recently developed a test to measure the emotional intelligence of…

A: Given,mean(μ)=95standard deviation(σ)=10

Q: Why does Mean of the Deviations Not a Useful Measure?

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Q: List a z score value that is three standard deviations away from the mean.

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Q: how do you find the standard deviation when the score is 9 points above tthe mean?

A: = population standard deviation = the size of the population = each value from the population =…

Q: Find the proportion of scores greater than 70 mean is 90 standard deviation is 10

A: The standard normal distribution:A continuous random variable Z is said to follow standard normal…

Q: The results of a common standardized test used in psychology research is designed so that the…

A: Consider X be a random variable which follows normal distribution indicating the score earned on a…

Q: The results of a common standardized test used in psychology research is designed so that the…

A: The standard normal value helps to understand the number of deviation of observations from the mean.…

Q: Because of a scoring error, 5 points were added to the test scores of everyone taking a final exams…

A: We have to find effect of error.

Q: Sarah's score on the second exam was 34 for which the mean of all scores was 28 and the standard…

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Q: ou find the standard deviation in the most easiest way?

A: The standard deviation is used to calculate the variability of the data set. It tells us about the…

Q: Change z-score (-2.00) into X value – Mean = 50, standard deviation = 10

A: Standard normal distribution: The standard normal distribution is a special case of the normal…

Q: A successful basketball player has a height of 6 feet 11 inches, or 211 cm. Based on statistics from…

A:

Q: IQ is normally distributed with a mean of 100 and a standard deviation of 15. What IQ do you need to…

A: IQ is normally distributed with a mean of 100 and a standard deviation of 15.

Q: How do I figure out snowfall is 98 inches per year and the standard deviation is 25 inches.  What…

A: We have to find percentage of the time does the city receive less than 125 inches.

Q: The mean score in a test is normally distributed with mean 30 and standard deviation 10. What is…

A: Given :  Mean, μ = 30 standard deviation, σ = 10 x = 55

Q: How does one calculate the standard deviation?

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Q: Explain an important difference between the standard deviation and the mean.

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Q: The Psych 230 students finished the course with a total population mean of 130 points and the…

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Q: basketball coach kept stats for his team in free throw percentage and steals (among others). At the…

A: Solution To find in which category did Erin do better compared with her team we will use z score.

Q: Isabel attends a fashion institute that has no on-campus housing. The distance she commutes between…

A: Given ,The  distance isabel's commutes between her home and the campus is , X = 19 kilometres.The…

Q: You have a data set with mean = 40 and standard deviation = 3. What can you say about the percentage…

A: Given  μ=mean=40, sd=σ=3 P(32<X<40)= ?  Note: this probability value calculated from standard…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!