Answer:
a. 0.0385
b. 3.44% probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean
and standard deviation 
In this question:

a. Calculate the appropriate standard error calculation for the data.

b. What is probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home?
This is 1 subtracted by the pvalue of Z when X = 0.5. So

By the Central Limit Theorem



has a pvalue of 0.9656
1 - 0.9656 = 0.0344
3.44% probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home