Marco runs a small dairy farm that also processes milk products on-site. One popular productproduced on the farm is a small bottle of cream. Marco knows that the volume of cream placedinto bottles is normally distributed, where the mean volume is 250 mL and standard deviationis 2.1 mL.(a) If Marco feels that a volume of cream less than 243.7 mL is too low to be sold, what proportionof bottles of cream produced were unfit for sale? Use the empirical rule to answer thisquestion.(b) Marco is thinking of developing a new product, which will involve adding a flavour to his cream.He thinks that bottles of cream above 255 mL will not be able to take the additional volume offlavouring and therefore will be unsuitable for sale. If 3700 bottles of cream were produced inthe last 6 months, how many bottles of cream would be unsuitable for sale as this flavouredproduct? Use the NORMDIST formula in excel to answer this question and give your answer tothe nearest bottle of cream.

a) Empirical rule: The probability of the observation lies within 1 standard deviation of the mean,…

Answered: Marco runs a small dairy farm that also…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Almost all medical schools require applicants to take the Medical College Admission Test (MCAT). To estimate the mean score of those who took the MCAT at WSSU, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 6.5. Suppose that (unknown to you) the mean score of those taking the MCAT at WSSU is 25.0. If you choose one student at random, what is the probability that the students scores is between 20 and 30?
The E&M 200 students took the exam, and the distribution of this data was bell- shaped. The average score was 68 and its standard deviation was 15. Using the empirical rule, 95% of the were between and If you scored 83 on the exam, what percentile are you in from the top? a. b.
Sheila's doctor is worried that she might develop gestational diabetes during her pregnancy. There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if their glucose level is above 140 mg/dl one hour after consuming a sugary drink. Sheila's measured glucose level one hour after the sugary drink varies according to the Normal distribution, with p = 125 mg/dl ando = 10 mg/dl. Fill in the following blanks with the correct options: (a) If a single glucose measurement is made, the probability that Sheila is diagnosed as having gestational diabetes is (0.0668, 0.1587, 0.2525, or 0.3173?). (b) Assuming that the population mean is 125 mg/dl, imagine that we repeat taking all possible samples of size 4 from the population, then only about 1.3 out of (10, 100, or 1,000?) sample means will have values as large as (125 or 140?) cm or even larger.
For all students who have taken a certain class during the last ten years, theaverage on the mid-term is 83.4 and the standard deviation of the mid-termscores is 7.2; the average on the final is 79.3 and the standard deviation of thescores on the final is 5.1; the correlation between scores on the mid-term andscores on the final is 0.86. 4. My teacher has lost our mid-term scores (but at least has our scores onthe final), so she is fitting a straight line to guess what we probably got onthe mid-term. What’s the equation of the line she is using? 5. I got a 90 on the final. What does my teacher think I got on the midterm?
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.8 parts/million (ppm). A researcher believes that the current ozone level is at an excess level. The mean of 242samples is 5.2 ppm with a variance of 1.001.00. Does the data support the claim at the 0.05 level? Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places. Specify if the test is one-tailed or two-tailed. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places. Make the decision to reject or fail to reject the null hypothesis.
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.97.9 parts/million (ppm). A researcher believes that the current ozone level is at an excess level. The mean of 2424 samples is 8.18.1 ppm with a variance of 0.250.25. Does the data support the claim at the 0.10.1 level? Assume the population distribution is approximately normal. Step 3 of 5: Specify if the test is one-tailed or two-tailed.
The weights of 1,000 men in a certain town follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds. From the data, we can conclude that the number of men weighing more than 165 pounds is about , and the number of men weighing less than 135 pounds is about .
Assume that you have been provided the following information for a sample of cars The covariance between weight and miles per gallon is equal to -4.9 pound-miles. The standard deviation of the cars' mileages is 7.75. The standard deviation of the cars' weights is 0.94. Estimate the correlation coefficient to the first decimal place.
A new Economic / Social Conservatism Scale has scores between 0 and 30 (0 being extreme liberal, 30 being extreme conservative). The mean score is 21 and standard deviation of scores is 5. You want to convert the original scale (call it X) to a new scale (call it Y) that has scores between 0 and 100. What is the correlation of X and Y?
The empirical rule states that the percentage of observations in a data set (provided that the data set has a bell-shaped and symmetric distribution) that fall within one standard deviation of their mean is approximately 75%. TRUE OR FALSE
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.9 parts/million (ppm). A researcher believes that the current ozone level is at an excess level. The mean of 24 samples is 8.1 ppm with a variance of 0.25. Does the data support the claim at the 0.1 level? Assume the population distribution is approximately normal. Step 5 of 5: Make the decision to reject or fail to reject the null hypothesis.
Two chemical companies can supply a raw material. The concentration of a particular element in this material is important. The mean concentration for both suppliers is the same, but you suspect that the variability in concentration may differ for the two companies. The standard deviation of concentration in a random sample of n₁ = 10 batches produced by company 1 is s₁ = 4.7 grams per liter, and for company 2, a random sample of n₂ = 16 batches yield s₂ = 5.8 grams per liter. Is there sufficient evidence to conclude that the two populations variances differ? Use a = 0.05. a. Because 0.321 < 0.657 <3.77, fail to reject the null hypothesis b. Because 0.265 < 0.657 <3.12, fail to reject the null hypothesis c. Because 0.386 < 0.657 <3.01, fail to reject the null hypothesis d. None among the choices

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