Question

Suppose that the average time that students spend online daily is normally distributed with a mean of 244 minutes and st dev of 49 minutes.  Answer the following questions.

1. What is the probability that a randomly picked student spends more than 265 minutes online daily?  Is this unusual, why or why not?

2. If a group of 21 students is randomly selected, what is the probability that their average time spent online is more than 265 minutes?  Is this unusual or not and why?

Answer 1

For first part, given the population is normally distributed, we will use z distribution with mean = 244 minutes and std. dev. = 49 minutes.

The probability a random student spends more than 265 minutes is 0.334 (calculator used is statcrunch, shown below)

This is not unusual, because typically a probability of less than 5% (means less than 0.05) is said to be unusual and ours is much higher than that.

For 2nd part, 21 samples are collected, n= 21

so, now we got a sampling distribution of means whose mean still remains 244, but standard deviation decreases because of multiple sampling. The standard deviation of mean of sampling distribution is called standard error (SE) and is equal to standard deviation of population (SD) divided by square root of n.

means SE = SD/ = 49 / = 10.6927

so that now, with mean = 244 and Std dev = 10.6927

probability of more than 265 is 0.0248 (approximately)

This is unusual as it is less than 0.05

If you are confused why the probability of more than 265 decreased drastically, then it is because of sample size. More the sample size, more precise our results are.

Thumbs up please!