Question

1. Apparently, depression significantly increases the risk of developing dementia later in life. In a recent study it was reported that of those who had depression, 22% (.22) went on to develop dementia, compared to only 17% (.17) of those who did not have depression. Suppose that 10% of all people suffer from depression.
   1. a. What is the probability of a person developing dementia?
      b. If a person has developed dementia, what is the probability that the person suffered from depression earlier in life?
      
      
   2. Cell phone talk time between charges is advertised as 10 hours. Assume that talk time is approximately normally distributed with a mean of 10 hours and a standard deviation of 0.75 hours.
      2a. Find the probability that talk time between charges for a randomly selected cell phone is above 11.35 hours.
      2.b. Your phone gets only about 8.35 hours of talk time, what proportion of phones gets less talk time than yours?

   3. 2.c. How much talk time would you get between charges, if you had a phone that get just into the top 1%?

Answer 1

1)

Lets say we have a sample size of 100

10% of all people suffer from depression = 10

of those who had depression, 22% (.22) went on to develop dementia

22% of 10 = 2.2

17% (.17) of those who did not have depression went on to develop dementia = 17% of 90 = 15.3

Probability is given by favorable/total

A)

Favorable = dementia = 15.3 + 2.2 = 17.5

Probability = 17.5/100 = 0.175

B)

Total = dementia = 17.5

Favorable = depression = 2.2

Probability = 2.2/17.5 = 0.12571428571