QMS Sheet

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Toronto Metropolitan University *

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210

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Statistics

Date

Feb 20, 2024

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pdf

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3

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What Formula to use: Q: The incomes of trainees at a local mill are normally distributed with a mean of $1,100 and a standard deviation of $150. What percentage of trainees earn less than $900 a month? Round your answer to the nearest hundredth of a percent. A: Normalcdf Q: Assume that the number of pieces of junk mail per day that a person receives in their mailbox follows the Poisson distribution and averages 4.3 pieces per day. What is the probability that this person will receive exactly four pieces of junk mail over the next two days? Round to four decimal places as needed. A: Poissonpdf Q: Based on a Comcast survey, there is a 0.8 probability that a randomly selected adult will watch prime-time TV live, instead of online, on DVR, etc. Assume that seven adults are randomly selected. Find the probability that fewer than three of the selected adults watch prime-time live. A: Binomcdf Q: A company has 125 personal computers. The probability that any one of them will require repair on a given day is 0.025. To find the probability that exactly 20 of the computers will require repair on a given day, one will use what type of probabilitydistribution? A: Binomial distribution Q: A professor receives, on average, 24.7 e-mails from students the day before the midterm exam. To compute the probability of receiving at least 10 e-mails on such a day, he will use what type of probability distribution? A: Poisson distribution Q: In its standardized form, the normal distribution has which of the following properties? A: Mean of 0, and standard deviation of 1 Qualitative and Quantitative: Qualitative: - Categorical - Nominal - Ordinal Nominal: - Can only be classified Ordinal: - Can only be classified and ordered
- E.x The possible responses to the question "Are you happy, indifferent, or unhappy with the performance per dollar spent on the Blu-ray player?" Quantitative: - Numerical - Interval - Ratio Interval: - Counts “0” as a form of measurement for e.x. Weather is 0 - Interval width = Highest value - lowest value / # of classes - E.x The possible responses to the question "In which year do you think the last recession in the United States started?" Ratio: - Do not count “0” as a form of measurement for e.x. Height cannot be “0” - E.x The possible responses to the question "How much time do you use the Blu-ray player every week on the average?" Definitions: Variance: CV = x 100 𝑆 𝑋 CV = x 100 σ µ Interquartile range: - Third quartile - first quartile Central tendency: - Mean, median, mode Right skewed: - Median is less than mode - The majority of the numbers are at the top in a stem and leaf plot Left skewed: - Median is greater than mode - The majority of the numbers are at the bottom in a stem and leaf plot The Empirical rule: - 68% of the values are within a distance of +1 standard deviation of the mean - 95% of the values are within a distance of +2 standard deviation of the mean - 99.7% of the values are within a distance of +3 standard deviation of the mean Example: - Population of 12 ounce cans of cola is known to have a mean fill weight of 12.06 ounces and a standard deviation of 0.02. The population is known to be bell shaped. Describe the distribution of fill weights. Is it very likely that a can will contain less than 12 ounces of cola?
+ = 12.06+0.02=12.04.12.08 µ σ + =12.06+2(0.02)=12.02.12.10 µ σ + =12.06+3(0.02)=12.00.12.12 µ σ Using the empirical rule, approximately 68% of the cans will contain between 12.04 and 12.08 ounces, approximately 95% will contain between 12.02 and 12.10 ounces, and approximately 99.7% will contain between 12.00 and 12.12 ounces. Therefore, it is highly unlikely that a can will contain less than 12 ounces. Sampling Distribution: Q: The Central Limit Theorem is important in statistics because A: For a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the distribution of the population.
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