Brienna Matson Assignment 10

Brienna Matson Seth Eikrem STAT243 Assignment 10 5-4 Pg/ 264 #12 Find these possibilities for a sample of 20 teenagers if 70% of them had compact disk players by the age of 16. A. At least 14 had CD players: 20!20-14!14!0.7¹⁴0.3⁶= 0.1916389828 ≈ 0.192 20!20-15!15!0.7¹⁵0.3⁵= 0.1788630506 ≈ 0.179 20!20-16!16!0.7¹⁶0.3⁴= 0.1304209744 ≈ 0.130 20!20-17!17!0.7¹⁷0.3³= 0.0716036722 ≈ 0.072 20!20-18!18!0.7¹⁸0.3²= 0.0278458725 ≈ 0.028 20!20-19!19!0.7¹⁹0.3¹= 0.0068393371 ≈ 0.007 20!20-20!20!0.7²⁰0.3⁰= 0.000797922663 ≈ 0.001 0.192 + 0.179 + 0.130 + 0.072 + 0.028 + 0.007 + 0.001 = 0.609 ≈ 61% B. Exactly 9 had CD players: 20!20-9!9!0.7⁹0.3¹¹= 0.0120066549 ≈ 0.012 ≈ 1.2% C. More than 17 had CD players: 20!20-18!18!0.7¹⁸0.3²= 0.0278458725 ≈ 0.028 20!20-19!19!0.7¹⁹0.3¹= 0.0068393371 ≈ 0.007 20!20-20!20!0.7²⁰0.3⁰= 0.000797922663 ≈ 0.001 0.028 + 0.007 + 0.001 = 0.036 ≈ 3.6%

D. Event A is most likely to occur because it has the highest probability of happening based on my calculations. 5-4 Pg.264 # 20 In a restaurant, a study found that 42% of all patrons smoked. If the seating capacity of the restaurant is 80 people, find the mean, variance, and standard deviation of the number of smokers. About how many seats should be available for smoking customers.

MEAN:

n × p = (80 × 40) = 33.6 people VARIANCE:

σ² = n × p × q = (80)(0.42)(0.58) = 19.488 ≈ 19.5 people STANDARD DEVIATION:

σ² =

19.5=4.4

I think about 39 seats should be available for smokers. Because the mean rounded up (34) + 1 standard deviation rounded up (5), is 39. It’s not that likely that there will be more than 39 smokers in the restaurant at once. (Or zero seats if it’s in Oregon because it’s illegal…)