JEOPARDY FOR CANDY YOU KNOW YOU WANT IT

Transcription

1 JEOPARDY FOR CANDY YOU KNOW YOU WANT IT

2 RULES 3 point categories: 250, 500, These represent: 1 piece, 2 pieces, 4 pieces of candy respectively. 5 topic categories: 2 related to normal dist, 1 sampling dist, 2 others. Person who answered the last question gets to decide what question everyone will work on. Questions are open to all to answer. This is a free-for-all, where nobody needs to form a group, but there are no restrictions on group size. But remember that candy belongs to the whole group...

3 Normality Ben loves normal Let s sample Dates Spicy

4 NORMALITY 250 Weights of potatoes are normally distributed. The mean is 0.3lbs, and 68% of potatoes have weights between 0.25 and 0.35 lbs. What is the SD of the potato weights, according to the empirical rule? 0.05 lbs.

5 NORMALITY 500 Suppose that time taken to finish the first STAT1030 midterm is normally distributed with mean 90 minutes and SD 13 minutes. Those who took longer than 2 hours did not finish the test. What proportion of students did not finish the test? 2 hours is 120 minutes, so P(X>120) = P(Z > (120 90)/13) = P(Z>2.31) = =

6 NORMALITY 1000 Suppose that from the time when Matt announced to hand in the mini-quiz, time taken to hand it in is normally distributed with mean 10 minutes and SD 2 minutes. Given a person took longer than 12 minutes to hand in the quiz, what is the probability the person took less than 15 minutes to hand it in? X = 12 => z = (12-10)/2 = 1; X=15 => z=(15-10)/2 = P X < 15 X > 12 = P X<15 X>12 (P X>12 = P 12<X<15 P X>12 2. (P X > 12 = 1 P X < 12 = 1 P Z < 1 = = (P 12 < X < 15 = P X < 15 P X < 12 = P Z < 2.5 P Z < 2 = = P X < 15 X > 12 = =

7 BEN LOVES NORMAL 250 Suppose that the theory part of the driver s license test has normally distributed test scores. If Ben s score of 21 was exactly at the 50 th percentile of scores, what is the mean of the distribution of scores? Since normal distribution is symmetric, the mean is the same as the 50 th percentile which is 21.

8 BEN LOVES NORMAL 500 The time it takes for Ben to walk to Schaeffer Hall from home is normally distributed with mean 17 minutes and SD 1 minute. Today s walk time is at the 89 th percentile in terms of how long it took. How long did Ben take? P(Z<z) = 0.89 => z = 1.23 x=z*σ+μ=1.23 * =18.23mins

9 BEN LOVES NORMAL 1000 When Ben was eating at the Riverside Casino buffet, the amount of crab that Ben eats is normally distributed with mean 2lbs and SD 0.2lbs. (Shell weight included, Ben is not actually a monster) Find the interquartile range of Ben s consumption of crab. Interquartile range is distance between 75 th and 25 th percentiles. P(Z<z) = 0.75 => z = 0.67=> x = 0.67 * = 2.134lbs By symmetry P(Z<z) = 0.25 => z = => x = * = 1.866lbs IQR = = 0.268lbs

10 LET S SAMPLE 250 Suppose Starburst candies have an average weight of 0.23oz and SD of 0.01oz. What is the expected weight of the sample average of 900 candies? Expected weight of a sample average is the same as the original distribution, which is 0.23oz.

11 LET S SAMPLE 500 People s heights have a normal distribution with mean 67 inches and SD 2 inches. A sample average of 100 people s heights would have follow what distribution? (state the type and parameters) തX N Mean = μ, SD = σ n = N 67, = N(67, 0.2)

12 LET S SAMPLE 1000 Suppose Ben on average spends 5 minutes grading a homework, with SD of 1.5 minutes. We can NOT assume the times are normally distributed. What is the probability that Ben takes a total of 5.5 hours or more grading 60 homework papers? (Hint: relate it to a sampling distribution.) x i = x, ҧ so expressing in minutes, n P X i > 330 = P( തX > 5.5). Since n > 30, by CLT a N(mean = 5, SD = ) Therefore P തX > 5.5 P Z > = P Z > 2.58 = =

13 DATES 250 My second brother registered for marriage on the luckiest day in What was the date? (lucky here is from a modern perspective.) 11/11/11.

14 DATES 500 Guess the year that Ben was born in? 1994.

15 DATES 1000 What is the date that the first discussion for STAT1030 for this semester was held? 8/24/2017.

16 SPICY 250 This herb has a pretty strong smell, and is used in guacamole and Thai cooking. Name the herb? Cilantro.

17 SPICY 500 Together these two herbs are often used for roasting poultry. Name the two herbs? Rosemary and thyme.

18 SPICY 1000 Indian spice, has two words in its name. First word is the same as the Malay word for salt, and the second is a common Indian restaurant name. Used to make chicken tandoori. Name the spice? Garam masala.