The mean score of all pro golfers for a particular course has a mean of 70 and a standard deviation of 3.0. Suppose 36 pro golfers played the course today. Find the probability that the mean score of the 36 pro golfers exceeded 71.

Q: The scores on the board are Normally distributed with a mean of 67 and a standard deviation of 13.…

A: From the provided information,X~N (67, 13)The bottom 5% of students will fail.

Q: A brother and sister took two different standardized tests.  He scored 114 on a test that had a mean…

A: Given that, A brother and sister took two different standardized tests.  He scored 114 on a test…

Q: The mean score on a set of 25 tests is 76. What is the sum of all the test​ scores?

A: The mean (aka the arithmetic mean, different from the geometric mean) of a dataset is the sum of all…

Q: You throw a ball as far as you can 5 times, recording the distance for each throw: 165 feet, 184…

A: since only 5 observation is given we will consider them as sample (n = 5)and population (N = 100)…

Q: The mean marathon finishing time for men and women was 268 minutes and 280 minutes respectively.…

A: From the given information, The mean marathon finishing time for men and women was 268 minutes and…

Q: A statistics professor gave a final exam to a class of 30 students. The exam scores are normally…

A: Given,mean(μ)=75standard deviation(σ)=10

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 recent poll found that 59% of adults believe the state of moral values is poor. For 400 randomly…

A: Here, n = 400 and p = 0.59

Q: what if the standard deviation was 30, instead of 60

A:

Q: The weights of men in their 30s are normally distributed with a mean of 190 pounds and a standard…

A: From the provided information, Population mean (µ) = 190 pounds Population standard deviation (σ) =…

Q: The test scores in a class are normally distributed with a mean score of 77. if the standard…

A: The distribution of test score are normally distributed with mean of 77. Now consider the standard…

Q: there are 300,000 people review  for the movie  pupulation mean is 7.2 stars and standard deviation…

A:

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: Justin got a score of 85 on an GE MMW examination for which the mean is 75. Justin realized that the…

A: Considering the mean score in the specified examination as μ and variance of scores in the…

Q: The test scores are normally distributed with a mean of 78 and a standard deviation of 9. If 39…

A: Obtain the probability that the average score is between 80 and 84. The probability that the average…

Q: A flu test shows that about 31% of 90 patients visited hospital in the first week of January had…

A: Given that  n = 90 , p = 31% = 0.31 , q = 1 - p = 1 - 0.31 = 0.69 X ~ Binomial (n = 90 , p = 0.31) X…

Q: The time taken to boil a kettle is normally  distributed with a mean of 94 seconds and  a standard…

A: The provided information is  µ=94 σ=6 P(-a<X<a)=0.40…

Q: When we _____ , it means that we have evidence of a statistically significant difference between the…

A: In hypothesis testing, we start with two opposing statements or hypotheses:1. Null Hypothesis : This…

Q: 5 students were given a test. The average and standard deviation of the 5 scores were found to be…

A:

Q: 7 of 14 Chihuahuas have a mean weight of 5.2 pounds, with a standard deviation of 1.2 pounds. German…

A:

Q: A data set has size of 40. How many observations lie within two standard deviations of either sides…

A: The 68-95-99.7% (Empirical) Rule: For a normal distribution, the empirical rule (68-95-99.7% Rule)…

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

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

Q: Explain with an example of the distribution of values around the mean by using general rules.…

A: We have to find given distribution.

Q: Write a sentence in your lab report explaining the effect that adding the two new data points had on…

A: From the given information,Original data points = {60,31,50,48,50,54,56,62,53}New additional points…

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

A:

Q: A recent survey found that 61​% of all adults over 50 wear glasses for driving. In a random sample…

A: A recent survey found that 61​% of all adults over 50 wear glasses for driving. In a random sample…

Q: If 70 shafts are sampled at random from the batch, what is the probability that the mean diameter of…

A: Let X be the random variable of the diameter of metal shafts produced in a manufacturing…

Q: In my Biology Class, to pass the course the minimum score must be 67. Biology class has a mean of…

A: Let, X= scores of the biology class Given that X follows a normal distribution with mean= 81 and…

Q: If a set of numbers has a standard deviation of zero, what can you say about the numbers?

A: The standard deviation indicates that amount of deviation of data points from the mean.

Q: An ABC new report stated that the mean distance that commuters in the United States travel each way…

A: Given : μ = 16 , σ= 8 and n= 75

Q: A set of math test scores has a mean of 70 and a standard deviation of 8.  A set of English test…

A: Consider that the mean and standard deviation of a random variable x are µ and σ, respectively.…

Q: The mean of a test score was 21.2 and the standard deviation was 5.1 . Identify the rest scores that…

A: Given Data Mean µ= 21.2. Standard Deviation σ= 5.1. Assuming that the given data is obtained from a…

Q: d the probability that a score is from 185 to 210. d the probability that a score is from 160 to…

A: As per your request I have solve only (d) option Given Mean =201 Standard deviations=21

Q: A large chemistry course took their final exam. The mean was 75 with a standard deviation of 8. What…

A: Let us define the random variable , X. Let X represent the final exam scores. Here X follows Normal…

Q: The temperature recorded at 60 airports in a region had a mean of 67 degrees Fahrenheit and a…

A:

Q: The highway mileages of 147 cars are in a file named CARS2.+ These cars are 2003 models. Find the…

A: Mean Formula The mean formula is defined as the sum of the observations divided by the total number…

Q: he mean score on a set of18 tests is 79.What is the sum of all the test​ scores?

A: Since we know that if a1,a2,.......an are numbers , then mean of all numbers is given by…

Q: aking the Graduate Management Aptitude Test averaged 812 with a standard deviation of 145. Only…

A: Given: Meanμ=812Standard deviationσ=145 Consider, X be the random variable that shows the average…

Q: When Christian runs the 400 meter dash, his finishing times are normally distributed with a mean of…

A:

Q: Left handed & right handed players on a baseball team Nominal Ordinal Interval Ratio

A: There are two types of data: Quantitative and Qualitative, Quantitative data is a set of values…

Q: Americans (on average) individually eat 16 pounds of seafood each year with a standard deviation of…

A: Given that   x̄ = 14 , μ = 16 , ? = 7 , n = 4

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!