Math Answers

When do we add the two corresponding areas of the z-score?

In an experiment of tossing a fair coin three times, find the P(X=2), P(X > 1) and P(1 ≤ X < 2). Let X be the random variable giving the number of tails.

The number of customers arriving per day at a certain automobile service facility is assumed to follow a Poisson Distribution with mean λ=20. Use normal approximation to find the probability that in a given day.

a) less than 25 customers will arrive;

b) at least 10 customers will arrive;

c) between 15 and 19 inclusive will arrive;

Suppose that X is a binomial random variable with n = 100 and p = 0.1

a) compute the exact probability that X is less than 4.

b) approximate the probability that X is less than 4 and compare to the result in part (a).

c) approximate the probability that 8 < X < 12

A process yields 10% defective items. If 100 items are randomly selected the process, use normal approximation to find the probability that the number of defectives.

a) exceeds 13 and

b) less than 8.

The heights of 1000 students are normally distributed with a mean of 174.5 centimeters and a standard deviation is 6.9 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, how many of these students would you expect to have heights.

a) less than 160.0 centimeters?

b) between 171.5 and 182.0 centimeters inclusive?

c) equal to 175.0 centimeters?

d) greater than or equal to 188.0 centimeters?

A company pay its employees an average wage of $15.90 an hour with a standard deviation of $1.50 , if the wages are approximately normally distributed and paid to the nearest cent,

a) what percentage of the workers receive wages between $13.75 and $16.22 an hour inclusive.

b) The highest 5% of the employee hourly wages is greater than what amount?

What level of measurement is required for this qualitative variables?

The IOs of 600 applicants to a certain college are approximately normally distributed with a mean of 115 and a standard deviation of 12. If the college requires an IQ of at least 95, how many of these students will be rejected on this basis, regardless of their qualifications? Note that IQs are recorded to the nearest integers.

For a car travelling 60 km per hour (kph), the distance required to brake to stop is normally distributed with mean of 20 meters and a standard deviation of 3 meters. Suppose you are travelling 60 kph in a residential area and a car moves abruptly into your path at a distance of 25 meters.

a) if you apply your brakes, what is the probability that you will brake to a stop within 18 meters or less?

b) if the only way to avoid a collision is to brake to a stop, what is the probability that you will avoid the collision?