Question

In a population of 20 cars, 9 of the cars have 4-cylinder engines.

Suppose we are interested in the proportion of car models that have 4 cylinders in the population.

Suppose it is known than about 50% of all car models have 4 cylinders.

Find the probability of randomly selecting a sample of 20 car models that contains more than nine (9) 4-cylinder cars.

Answer 1

Solution: We can use here Binomial probability distribution to find the mentioned probability.

We are given:

Let be the number of cars having 4 cylinders.

We have to find

We know the Binomial probability distribution model is:

Using the same model in above individual probabilities, we have:

Hence the probability of randomly selecting a sample of 20 car models that contains more than nine (9) 4-cylinder cars is

We can also use excel to find this probability:

Now using excel we have: