A headline in a certain newspaper states that "most stay at first job less than 2 years."
That headline is based on an online poll of 320 college graduates. Among those polled,
72% stayed at their first full-time job less than 2 years. a. Assuming that 50% is the true
percentage of graduates who stay at their first job less than two years, find the mean and
standard deviation of the numbers such graduates in randomly selected groups.
I know how to get the mean and standard deviation I am just not sure how to do it in this problem. I have been trying to figure it out for two hours
how so you find the margin of error and the interval estimate
I was wondering how to do this too please someone answer.:(((
To calculate the mean and standard deviation of the numbers of graduates who stay at their first job less than two years in randomly selected groups, we can use the binomial distribution.
In this case, the binomial distribution can be used because each graduate in the poll can be considered a Bernoulli trial (a trial with two possible outcomes: staying at the first job less than two years or staying longer). The probability of success (p) is assumed to be 0.5, representing the true percentage of graduates who stay at their first job less than two years.
First, let's calculate the mean:
The mean of a binomial distribution is given by the formula:
mean = n * p
In this case, n represents the sample size (the number of randomly selected groups) and p represents the probability of success.
To find the mean, we need to know the sample size. Let's say the sample size is denoted by "x."
mean = x * 0.5
Next, let's calculate the standard deviation:
The standard deviation of a binomial distribution is given by the formula:
standard deviation = sqrt(n * p * (1 - p))
Using the same sample size (x):
standard deviation = sqrt(x * 0.5 * (1 - 0.5))
Once you have the actual sample size (x), you can substitute it into the equations to compute the mean and standard deviation.
Please note that the values obtained will be based on the assumption that the percentage of graduates who stay at their first job less than two years is exactly 50%, which may not reflect the true population value.