Statistics Exam Distribution and Probability Problems Guide

Multiple Choice 5 points Answer Q.1 and Q.2 based on the following information. The histogram shown below represents 40 student scores on a statistics exam. Which of the following best describes the shape of the following data distribution? It's a right-skewed distribution. It's a left-skewed distribution. It's a symmetric distribution. It's a unimodal distribution. It's a bimodal distribution. 1

Multiple Choice 5 points What proportion of the scores are below 60? Give your answer to three decimal places. 0.125 0.225 0.325 0.425 0.525 2

Multiple Choice 5 points The boxplot below shows the amount of time it takes Melina to run a mile. A summary of that data is one of the options below. Select which data set summary best matches the boxplot. Mean=5.5 Std Dev=5 Median=6.5 Mean=5.5 Std Dev=8 Median=6.5 Mean=7.5 Std Dev=6 Median=7.5 Mean=5.5 Std Dev=4 Median=5.5 3

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Mean=6 Std Dev=1 Median=5.5 Multiple Choice 5 points Answer Q.4-Q.7 based on the following information. Compute the median of the following dataset: 10, 12, 12, 14, 14, 16, 16, 20, 22, 23, 23, 24, 25, 25, 27, 30, 35 21 21.5 22 22.5 23 4

Multiple Choice 5 points Compute the ±rst quartile or, the 25-th percentile of the above dataset using the method discussed in class. 11 12 13 14 15 5 Multiple Choice 5 points Compute the third quartile or, the 75-th percentile of the above dataset using the method discussed in class. 23 24 25 26 27 6

Multiple Choice 5 points Compute the inter-quartile range of the above dataset. 10 10.5 11 11.5 12 7 Numeric 5 points Answer Q.8-Q.14 based on the following information. The probability that a ±rm will open a branch of±ce in Toronto is 0.7, that it will open one in Mexico City is 0.4, and that it will open an of±ce in either of the two cities is 0.8. Find the probability that the ±rm will open an of±ce in exactly one of the cities. 0.5 8

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Numeric 5 points Find the probability that the ±rm will open an of±ce in neither of the cities. 0.2 9 Numeric 5 points Find the probability that the ±rm will open an of±ce in Mexico city but not in Toronto. 0.1 10 Numeric 5 points Find the probability that the ±rm will open an of±ce in Toronto but not in Mexico City. 0.4 11 Numeric 5 points Find the probability that the ±rm will open their of±ces in both cities. 0.3 12

Numeric 5 points Find the probability that the ±rm will open their of±ces in none of the cities. 0.2 13 Numeric 5 points Find the probability that the ±rm will NOT open their of±ces in both the cities. 0.7 14 Numeric 5 points When my daughter goes to school there is a 72% probability that she will forget her lunchbox. When my youngest son goes to school there is a 27% probability that he will forget his lunchbox. If either my daughter or my son forget their lunchbox my wife has to go down to the school to give it to them. Assuming these two kids act independently of each other, what is the probability that my wife will need to go to their school on a random day? Answer up to four decimal places. 0.7956 15

Multiple Choice 5 points Poker is a card played with a standard 52 card playing deck. We draw one card at a time without replacement from the top of a shuf²ed standard poker deck and stop when we draw an ace. What is the probability that the game will be stopped after the ±fth draw? Answer up to four signi±cant places. Hint: Try to think in how many ways an Ace can be drawn for the ±rst time in the ±fth draw when cards are drawn, one by one, and without replacement. How many Ace cards and non-Ace acrds are there? What would be the total number of ways in which you can draw ±ve cards, one by one, and without replacement from a deck of 52 cards? 0.0299 0.0399 0.0499 0.0599 0.0699 16

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Multiple Answer 5 points Consider two events and with , and . Then and are independent if (select all that apply): If the ocuurence or, the non-occurence of one of them doesn't have any impact on the occurrence or, the non-ocuurence of the other. and are independent of each other. 17 Numeric 5 points In College Station there are a lot of old houses. If a house was built before 1980 there is a 26% chance it will have galvanized steel plumbing. If it was built after 1980 then there's a 15% chance it will have galvanized steel plumbing. Note that 50% of the houses in College Station were built before 1980. Suppose I select a random house and discover it has galvanized steel plumbing. What is the probability it was built before 1980? Answer up to four decimal places. Hint: Use Bayes' Theorem. 0.634146 18

Numeric 5 points Answer Q.9-Q.12 based on the follwoing information. A EI247 weapon ±res 7 bullets automatically at a target 1,940 meters away. The number of bullets, say, , that will hit the target is random, with a PMF shown below: Find the value of that makes the above function a valid probability mass function (PMF). Report your answer up to ±ve decimal places. 0.48387 19 Numeric 5 points What is the probability that a random ±ring of EI247 would result in fewer than 1 bullets hitting the target? Report up to ±ve decimal places. 0.09677 20

Numeric 5 points Compute the expected number of bullets resulted in by a random ±ring of EI247. Answer up to ±ve decimal places. 3.70967 21 Numeric 5 points What is the probability that a random ±ring EI247 would result in at least 2 bullets but fewer than 5 bullets? Report up to ±ve decimal places. 0.403225 22

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Multiple Choice 5 points Answer Q.13 and Q.14 based on the following information. When it rains the River Kwai rises a random amount, say, , whose distribution given by the probability density function (PDF) below: Find the cumulative distribution function (CDF) of . 23

Numeric 5 points What is the probability that the river will rise more than 2.59 which is when it will break the bridge? Use up to 5 decimal places. 0.42063 24

Multiple Choice 5 points Suppose is a continuous random variable with density function given by Select the CORRECT statement about the distribution of from the following. , because it's a probability. The constant must be 5 so that is a valid probability density function. 25 Numeric 5 points If I walk into the steam room at the Rec Center randomly (when no one has been in there) the temperature is normally distributed with a mean of 102 and a standard deviation of 12. If the temperature is so low that it's in the lowest 13% then I'll turn the heat back on. At what temperature will I be turning the heat on? What is the z-score you would use to answer this? Answer up to two decimal places. -1.13 26

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Numeric 5 points What is the temperature that marks the coldest 13%? Round up to two decimal places. 88.44 27 Multiple Choice 5 points The age at which a person prefers the "Oldies Music" station (a sure sign of becoming old) is normally distributed with a mean of 62 and standard deviation of 1.4. If I randomly pick someone and track them what is the probability they will start to prefer the "Oldies Music" at age 60 or younger? Answer up to ±ve decimal places. 0.00656 0.03656 0.05656 0.07656 0.09656 28

Numeric 5 points The distribution for how long a cell phone can be in the water (in milliseconds) before being ruined has the following moment generating function (MGF): being some small positive real number. Compute the second order moment of the given probability distribution. 504 29 Numeric 5 points Some civil engineers are modeling the projected load on a new bridge as where , and are independent random variables with means , and standard deviations , respectively. Determine the standard deviation of up to four decimal places. 8.7224 30

STAT 211 End-term Practice Problems, Fall 2023 - Set 2 (Answer Keys)

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