Mathematics

MTH 23 – Homework 4 Due: Tuesday April 25
1. A die is tossed 3 times. What is the probability of
a) No fives turning up? b) One five? c) Three fives?
2. A manufacturer of metal pistons finds that on the average, 15% of his pistons are rejected because they are
either oversize or undersize. What is the probability that a batch of 10 pistons will contain
a) No more than 2 rejects? b) At least two rejects?
3. The director of a health club conducted a survey and found that 20% of members used only the pool for
workouts. Based on this information:
a) What is the probability that for a random sample of 10 members, 4 used only the pool for workouts?
b) Calculate the expected number of members who used only the pool for workout and standard deviation, if
a random sample of 50 members is chosen.
4. Hospital records show that of patients su↵ering from a certain disease, 75% die of it.
a) What is the probability that of 6 randomly selected patients, at least 4 will recover?
b) Calculate the expected number of recovery and standard deviation, if 10 patients are randomly selected.
5. The random variable x is normally distributed with mean µ = 30 and standard deviation ! = 4. Find
a) P (x < 40)
b) P (x > 21)
c) P (30 < x < 35)
6. A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a
mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car picked at random
is traveling at more than 100 km/hr?
7. For a certain type of computers, the length of time between charges of the battery is normally distributed
with a mean of 50 hours and a standard deviation of 15 hours. John owns one of these computers and wants
to know the probability that the length of time will be between 40 and 70 hours.
8. The heights of 18-year-old men are normally distributed with mean 68 inches and standard deviation 3 inches.
a) What is the probability that a randomly selected 18-year-old man is between 67 and 69 inches tall?
b) If a random sample of nine 18-year-old men is selected, what is the probability that the mean height is
between 67 and 69 inches?
9. Suppose the life span of English Springer Spaniel dogs is normally distributed with a mean of 13 years and a
standard deviation of 1.5 years.
a) What is the probability that a randomly selected English Springer Spaniel will live to be 14 years or older?
b) What is the probability that a randomly selected sample of 25 English Springer Spaniels will have a mean
life span of 14 years or more?
c) What is the probability that a randomly selected sample of 25 English Springer Spaniels will have a mean
life span between 12.5 and 14 years?