Aaron and Jonathan take turns shooting a free throw, with Aaron going first. Whoever makes the first shot wins. The game continues until someone makes the shot. Aaron has a 40% chance of making a free throw, while Jonathan has a 50% chance. What is Aaron's chance of winning the game?

Question

Paddington

Mathematics

9 November, 14:45

Aaron and Jonathan take turns shooting a free throw, with Aaron going first. Whoever makes the first shot wins. The game continues until someone makes the shot. Aaron has a 40% chance of making a free throw, while Jonathan has a 50% chance. What is Aaron's chance of winning the game?

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Answers (1)

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Nikolas Spencer · Answer 1

a) 15.58

b) 39.06

Step-by-step explanation:

MENSA is organization whose member have IQs in the top 2% of the population. IQs are normally distributed with mean 100, and the minimum IQ score required for admission to MENSA is 132.

From standard normal table z value for top 2% = 2.054

132 = 100+2.054*σ

σ = (132-100) / 2.054=15.58

(b) Cholesterol levels for women aged 20 to 34 follow an approximately normal distribution with mean 185 milligrams per deciliter (mg/dl). Women with cholesterol levels above 220 mg/dl are considered to have high cholesterol and about 18.5% of women fall into this category.

From standard normal table z value for top 18.5% = 0.896

220 = 185+0.896*σ

σ = (220-185) / 0.896 = 39.06