Geometric Random Variables Assignment
Eighteen percent of apples grown in an orchard have defects. Let X = the number of apples that are randomly inspected from the orchard until a defective one is found. What is the probability that the first defective apple found is the 10th one inspected? Round to 2 decimal places.
0.03
Marshall spins a prize wheel with 4 segments of equal size, one of which is labeled "winner." Let X = the number of spins until Marshall wins a prize. What is the probability that Marshall wins a prize on his 2nd spin? Recall: P(X = k) = (1 - p)k-1p Round to 4 decimal places
0.1875
Eighteen percent of apples grown in an orchard have defects. Let X = the number of apples that are randomly inspected from the orchard until a defective one is found. What is P(X ≤ 4)? Round to 3 decimal places.
0.548
Five percent of canned goods get bumps or dents in the cans during manufacturing. Let X = the number of cans that are inspected before one with a bump or dent is found. What is the probability that more than 3 cans are inspected before one with a bump or dent is found? Round to 4 decimal places.
0.8574
Forty-five percent of customers at a grocery store use a coupon. Let X = the number of customers selected at random before one is found who will use a coupon. What are the mean and standard deviation of X? Round each answer to 3 decimal places.
2.222; 1.648
Five percent of canned goods get bumps or dents in the cans during manufacturing. Let X = the number of cans that are inspected before one with a bump or dent is found. What is the mean and standard deviation of X? Mean = _____ Standard Deviation = _____
20; 19.494
Eighteen percent of apples grown in an orchard have defects. Let X = the number of apples that are randomly inspected from the orchard until a defective one is found. Check the conditions to determine if this is a geometric setting. 1. Are the outcomes binary? _____ Success/Failure: ________ 2. Are the trials independent? _____ 3. Are we counting the number of trials to obtain the first success? ____ 4. Is the probability of success the same for each trial? _____
Yes; defect, no defect; yes; yes; yes, p = 0.18
Carlos draws cards from a standard deck of cards, replacing the card each time and shuffling until he draws a red card. Let X = the number of red cards drawn within the first 10 draws. Check the conditions to determine if this is a geometric setting. 1. Are the outcomes binary? _____ Success/Failure: ________ 2. Are the trials independent? _____ 3. Are we counting the number of trials to obtain the first success? ____ 4. Is the probability of success the same for each trial? _____
Yes; red, not red; yes; no; yes, p = 0.5
Marshall spins a prize wheel with 4 segments of equal size, one of which is labeled "winner."Let X = the number of spins until Marshall wins a prize. Check the conditions to determine if this is a geometric setting. 1. Are the outcomes binary? _____ Success/Failure: ________ 2. Are the trials independent? _____ 3. Are we counting the number of trials to obtain the first success? ____ 4. Is the probability of success the same for each trial? _____
Yes; win, do not win; yes; yes; yes, p = 0.25
