An air force intercept squadron consists of 16 planes that should always be ready for immediate launch. However, a plane's engine can be troublesome, and there is a probability of .25 that the engines of a particular plane will not start at a given attempt. if this happens, the mechanic ,must wait 5 minutes before trying to start with the engines again. The squadron commander is interested in how many planes will immediately become airborne if the squadron is scrambled. Find the expected number of planes that would be successfully launched (the mean), the variance, the standard deviation, the probability that exactly 12 planes scramble successfully and the probability that at least 14 planes scramble successfully.

(a) The mean, variance and standard deviation of planes that would be successfully launched are 12, 3 and 1.732 respectively.

(b) The probability that exactly 12 planes scramble successfully is 0.225.

(c) The probability that at least 14 planes scramble successfully is 0.1971.

Step-by-step explanation:

Let X = number of planes whose engines will start at the first attempt.

The probability of X is:

P (A plane starting immediately) = 1 - P (A plane not starting at the 1st attempt)

                                                     = 1 - 0.25

                                                  p = 0.75

The number of planes at the air force intercept squadron is, n = 16.

The random variable X follows a Binomial distribution, i.e.

(a)

The expected value of a Binomial distribution is:

Compute the expected number of planes that would be successfully launched as follows:

The variance of a Binomial distribution is:

Compute the variance of planes that would be successfully launched as follows:

Compute the standard deviation of planes that would be successfully launched as follows:

Thus, the mean, variance and standard deviation of planes that would be successfully launched are 12, 3 and 1.732 respectively.

(b)

The probability function of a Binomial distribution is:

Compute the probability that exactly 12 planes scramble successfully as follows:

Thus, the probability that exactly 12 planes scramble successfully is 0.225.

(c)

Compute the probability that at least 14 planes scramble successfully as follows:

P (X ≥ 14) = P (X = 14) + P (X = 15) + P (X = 16)

Thus, the probability that at least 14 planes scramble successfully is 0.1971.

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

answer: b.

step-by-step explanation:

the y coordinate for point b is 0, and answer b is the only one with that y coordinate.