ProbClass[1a] - X of Z: What's the # of times guys are...

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X of Z: What’s the # of times guys are rejected at a certain nightclub? At a certain nightclub, the mean # of times ( ie.µ) men are rejected is 7 with a standard deviation of 1.5.(ie. ó) We want to know the rejection rate that is, say, 75% of all men are equal to or less than? First, instead of doing z score, draw your curve from 0 to 100%(ie. empirical rule). Second, see if percentage is above or below 50%.
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X of Z continued… Since 75% is above 50%, you know z score must be positive. Since 75% crosses µ, you know you need the ‘Big Part’. Z=.68. Now we just solve for X; X= µ+z(ó) 75% and the ‘Big Part’ is associated with a Z score of .68. X= 7+.68(1.5)= 8.02 is the rejection rate that 75% of men are equal to or less; What about for 35% of men?? Since z is below 50%, Z must be negative. Since 35% doesn’t cross µ, you know you need ‘Small Part’
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Solving for 35% X= µ+z(ó) When z score has to be subtracted, start with this value. 35% and the ‘Small Part’ is associated with a Z score of .38. –Z(ó) +µ –.38(1.5) +7= 6.43 6.43 is the rejection rate that 35% of men are equal to or less than;
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Review of Simple Probability The probability of a simple event is a ratio of the number of favorable outcomes for the event to the total number of possible outcomes of the event. The probability of an event a can be expressed as: ( 29 outcomes possible of number total outcomes favorable of number = a P
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Find Outcomes of simple events For Simple Events – count the outcomes Examples: One Die- 6 outcomes One coin- 2 outcomes One deck of cards- 52 outcomes; 4 Aces, 12 face cards, and 36 non-face cards(ie 2-10); U.S. Roulette Wheel- 38 total slots, 18 red, 18 black, and 2 green;
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Basic Probabilities What is the probability of getting a red on a U.S. roulette wheel? 18 red slots, 18 black slots, and 2 green slots. Solution: Desired outcome divided by # of possible outcomes=18/38, .474 or a 47.4% chance of landing on red; What is the probability of drawing a black ace from a deck of cards; 2/52= .0385 or 3.85%
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Compound Events Events that cannot occur at the same time are called mutually exclusive. Suppose you want to find the probability of
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ProbClass[1a] - X of Z: What's the # of times guys are...

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