Question

In: Math

Question: A set of data has a normal distribution with a mean of 53 and a...

Question: A set of data has a normal distribution with a mean of 53 and a standard deviation of 6. Find the...

A set of data has a normal distribution with a mean of 53 and a standard deviation of 6. Find the percent of data within each interval...

a. from 47 to 65

b. from 41 to 47

c. greater than 59

d. less than 65

Please show all steps.

Note: a - d are NOT potential answers, they are subquestions. I would like to know the percent of data within each interval in a, b, c, and d.

Please show all the work, including any calculator steps taken. Please do not say "use calculator" - specify what exactly to do with it if you do use it.

Solutions

Expert Solution

Given, mean of normal distribution is : m = 53 and standard deviation is : = 6.

Then, probability density function f(x) is :

i.e.,

a) Now, P(47<x<65) =

Taking we get,

= 0.8186

b) Now, P(47<x<65) =

Taking we get,

= 0.1359

c) Now, P(x>59) =

Taking we get,

= 1

d) Now, P(x<65) =

Taking we get,

= 0.9772

milcah answered 1 year ago

Next > < Previous

Related Solutions

A set of data has a normal distribution with a mean of 47 and a standard...

A set of data has a normal distribution with a mean of 47 and a standard deviation of 7. Find the percent of data within the following interval. less than 47

Question 4 (5 marks) Stock’s Blue annual profit follows a Normal distribution, with mean £53 and...

Question 4 Stock’s Blue annual profit follows a Normal distribution, with mean £53 and standard deviation £9. Stock’s Red annual profit follows a Normal distribution, with mean £62 and standard deviation £6. What is the probability that at a random year stock Blue will outperform stock Red? Your portfolio consists of 2 Blue stocks and 3 Red stocks. What is the probability that your profit will exceed £330?

(6) 2. A data set has a distribution that is skewed left with a mean of...

(6) 2. A data set has a distribution that is skewed left with a mean of 88 and a standard deviation of 22. I take 30,000 samples each of size 20 from this data set. Then the sampling distribution of sample means will have a) Mean = _______ b) standard deviation = ____________ c) What shape distribution? __________ (8) 3. The number of miles driven on trips for Thanksgiving is normally distributed with a mean of 120 miles and a...

A population of values has a normal distribution with μ=6.8 and σ=53. A random sample of...

A population of values has a normal distribution with μ=6.8 and σ=53. A random sample of size n=197 is drawn. Find the probability that a single randomly selected value is between 4.5 and 17. Round your answer to four decimal places. to find answer P(4.5<X<17)= Find the probability that a sample of size n=197 is randomly selected with a mean between 4.5 and 17. Round your answer to four decimal places. to find answer P(4.5<M<17)=

Data Analysis and Probability: For Questions 6-7: A normal distribution has a mean of 2.5 and...

Data Analysis and Probability: For Questions 6-7: A normal distribution has a mean of 2.5 and a standard deviation of 0.6. Find the probability that a randomly selected x-value from the distribution is in the given interval. Round your decimal answer to the nearest hundredth and your percent to the nearest whole number. 6) Between 3.3 and 3.9 7) At least 2.1 8) After sending, the email of a certain system has normally distributed arrival times with a mean of...

QUESTION 27 In a normal distribution of scores with a mean of 35 and a standard...

QUESTION 27 In a normal distribution of scores with a mean of 35 and a standard deviation of 4, which event is more likely; a) a randomly selected score is between 29 and 31 or b) a randomly selected score is between 40 and 42? Explain your response in 2-3 sentences.

The data below is suspected to be part of a normal distribution - unknown mean and...

The data below is suspected to be part of a normal distribution - unknown mean and variance. perform goodness of fit test to confirm if the data really comes from a normal distribution. a) Estimate the normal distribution: b) Partition the range of the data into 4 mutually exclusive intervals. c) Calculate the relative frequency of each interval you selected using the observed data. d) Calculate the theoretical probabilities of the intervals you selected assuming the data came from a...

Check if the following data set corresponds to normal distribution or not? Life Expectancies for Men...

Check if the following data set corresponds to normal distribution or not? Life Expectancies for Men in European Countries in 2011: 73 79 67 78 69 66 78 74 71 74 79 75 77 71 78 78 68 78 78 71 81 79 80 80 62 65 69 68 79 79 79 73 79 79 72 77 67 70 63 82 72 72 77 79 80 80 67 73 73 60 65 79 66

Question 37: The distribution of SAT scores is normal with a mean of µ = 500...

Question 37: The distribution of SAT scores is normal with a mean of µ = 500 and a standard deviation of σ = 100. What SAT score (i.e., X score) separates the top 25% of the distribution from the rest? What SAT score (i.e., X score) separates the top 40% of the distribution from the rest? What SAT score (i.e., X score) separates the top 4% of the distribution from the rest?

A population parameter has a normal distribution and has a mean of 45 and variance of...

A population parameter has a normal distribution and has a mean of 45 and variance of 15. From this population a sample is selected with a size of 19 and the variance of the sample is 17. Does this sample support the population variance? Evaluate.

Subjects