Answer:
The probability that at most 50 say that they drink coffee during exam week is 0.166.
Step-by-step explanation:
The random variable <em>X</em> can be defined as the number of college students who prefer to drink more coffee during the exams week.
The probability of the random variable <em>X</em> is <em>p</em> = 0.67.
A random sample of <em>n</em> = 80 college students are selected.
The response of every students is independent of the others.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 80 and <em>p</em> = 0.67.
But the sample selected is too large and the probability of success is close to 0.50.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
- np ≥ 10
- n(1 - p) ≥ 10
Check the conditions as follows:
Thus, a Normal approximation to binomial can be applied.
The mean of the distribution of <em>X</em> is:
The standard deviation of the distribution of <em>X</em> is:
A Normal distribution is a continuous distribution. So, the probability at a point cannot be computed for the Normal distribution. To compute the probability at a point we need to apply the continuity correction.
Compute the probability that at most 50 say that they drink coffee during exam week as follows:
Apply continuity correction:
*Use a <em>z</em>-table for the probability.
Thus, the probability that at most 50 say that they drink coffee during exam week is 0.166.
