ASSIGNMENT 5
2
2
2
1. Find the centroid of the
p solid bounded above by the sphere x + y + z = 4
2
2
and below by the cone z = x + y .
2. A fair die is rolled repeatedly five times. What is the probability that 1 turns
up exactly three times? What is the probability that 1 turns up at least three times?
3. If the probability of producing a defective lightbulb is p = 0.005, what is the
probability that o lot of 2000 lightbulbs will contain more than six defectives?
4. If the lifetime X of a certain kind of automobile battery is normally distributed
with mean of 4 yr and a variance of 1 yr, and the manufacturer wishes to guarantee
the battery for 3 yr, what percentage of the batteries is he expected to replace under
the guarantee?
5. Let X be a random variable with binomial distribution B(n; p). What is the
probability that X takes an even value?
Hint. Use the binomial formula (a + b)n = nk ak bn−k to express (p + q)n and (p − q)n ,
where q = 1 − p.
1