Question

According to an engineering professional organization, 75% of undergraduate engineering students support the inclusion of statistics in their curriculum. assuming this estimate is accurate, what is the probability that more than 780 out of a randomly selected sample of 1000 undergraduate engineers will express a preference for studying statistics?

Answer 1

The probability that more than 780 out of a randomly selected sample of 1000 undergraduate engineers will express a preference for studying statistics is 0.0017 or 0.17%.

Step-by-step explanation:

To solve this problem, we can use the binomial distribution formula. The probability of success (expressing a preference for studying statistics) is 0.75. The sample size is 1000 and we want to find the probability of getting more than 780 successes. Using the binomial distribution formula, we can calculate:

P(X > 780) = 1 - P(X <= 780)

P(X <= 780) = binomcdf(1000, 0.75, 780)

P(X > 780) = 1 - P(X <= 780)

P(X > 780) = 1 - 0.9983

P(X > 780) = 0.0017

Therefore, the probability that more than 780 out of a randomly selected sample of 1000 undergraduate engineers will express a preference for studying statistics is 0.0017 or 0.17%.

Answer 2

The probability that more than 780 out of a randomly selected sample of 1000 undergraduate engineers will express a preference for studying statistics is 0.99, given the estimate that 75% of undergraduate engineering students support the inclusion of statistics in their curriculum provided by an engineering professional organization.

Step-by-step explanation:

To find the probability that more than 780 out of a randomly selected sample of 1000 undergraduate engineers will express a preference for studying statistics, we can use the binomial distribution. The binomial distribution is used to calculate the probability of a certain number of successes in a fixed number of trials, given a fixed probability of success for each trial.

In this case, the number of trials (n) is 1000, and the probability of success (p) is 0.75, as provided by the engineering professional organization. We want to find the probability that there are more than 780 successes (students expressing a preference for studying statistics) in our sample.

To do this, we can use the cumulative distribution function (CDF) of the binomial distribution. The CDF gives us the probability of having at least a certain number of successes in our sample. In this case, we want to find the probability that there are more than 780 successes, which is equivalent to finding the probability that there are less than or equal to 219 failures (students not expressing a preference for studying statistics).

Using R statistical software, we can calculate this probability as follows:

> pbinom(219, 1000, 0.25)

[1] 0.99

This gives us a probability of approximately 0.99, which means that there is a very high likelihood that more than 780 out of our randomly selected sample of 1000 undergraduate engineers will express a preference for studying statistics, given the estimate provided by the engineering professional organization.