MATH116 3-31

Number Systems

100

Consider 321 in base 4. What is this in base 10? 

57

200

Consider 30 in base 10. Convert this to base 2. 

11110

300

Consider 2581 in base 10. Convert this to base 5. 

40311

Binomial Distributions

100

The probability of getting heads on an unfair coin is .7. What is the probability of flipping exactly 3 heads in 8 flips? 

.0467

200

The probability of rain each day is 30%. What is the probability it rains 4 of less times in the next 7 days? 

.971

300

The probability a salesman actually sells his product to each person is 35%. What is the probability that out of 20 people, he sells it to more than half of the people? 

.0532

Normal Distributions

100

The weights of a type of dogs are normally distributed with mean 60 lbs and standard deviation 8 lbs. What's the probability a dog weighs less than 50 lbs? 

.1056

200

The heights of American men are normally distributed with mean 69 inches and standard deviation 3.5 inches. What is the probability a man is between 65 inches and 72 inches tall?

.678

300

The time it takes to cook a pizza is normally distributed with mean 8 minutes and standard deviation .5 minutes. What's the probability it takes more than 10 minutes to cook a pizza? 

.000032

Doubling Time/Half Life

100

A population grows at 3% each year. Initially there are 1,200 in the group. What's the doubling time?

23.45 years

200

Every hour, 75% of a drug is expelled from the body. What is the half-life? 

.5 hrs/ 30 minutes

300

The half-life of a drug is 5 hours. How much of the drug is expelled each hour? 

29.29%