Answer:
a) 30.50% probability that at least 150 stay on the line for more than one minute.
b) 0% probability that more than 200 stay on the line for more than one minute.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:

The standard deviation of the binomial distribution is:

Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that
,
.
In this problem, we have that:

So


a. at least 150 stay on the line for more than one minute.
Using continuity correction,
, which is 1 subtracted by the pvalue of Z when X = 149.5. So



has a pvalue of 0.6950
1 - 0.6950 = 0.3050
30.50% probability that at least 150 stay on the line for more than one minute.
b. more than 200 stay on the line.
Using continuity correction,
, which is 1 subtracted by the pvalue of Z when X = 200.5. So



has a pvalue of 1
1 - 1 = 0
0% probability that more than 200 stay on the line for more than one minute.