Question

From the whole population of automobiles, 30% fail the emission test with the normal performance of a car. A manufacturer is selecting 15 cars to run through emission tests. Use the binomial cumulative distribution function to calculate the probability of each number of failures possible. From the distribution, how many cars can fail the test before we conclude there is a malfunction?

p =.30
X is the number of cars that fail the test out of 15.

Answer 1

To calculate the probability of each number of failures in a sample, we can use the binomial cumulative distribution function. This function calculates the probability of getting up to a certain number of failures in a given number of trials. We can then use the distribution to determine the number of cars that can fail the test before we conclude there is a malfunction.

Step-by-step explanation:

To calculate the probability of each number of failures possible, we can use the binomial cumulative distribution function. This function calculates the probability of getting up to a certain number of failures in a given number of trials.

In this case, the population of automobiles has a 30% failure rate. The manufacturer is selecting 15 cars for emission tests. We want to find the probability of each number of failures, from 0 to 15.

Using the binomial cumulative distribution function, we can calculate the probability for each number of failures. The number of failures can range from 0 to 15, so we calculate the probability for each value of X. The cumulative probability is found by summing up the individual probabilities for each value of X.

From the distribution, we can determine how many cars can fail the test before we conclude there is a malfunction. This would be the number of cars with failure probabilities that are considered significantly lower than the others.