Question

ccording to a recent study, the mean number of hours college students spent playing video games per month was 22 hours with a population standard deviation of 2 hours. Two weeks before final exams were scheduled to begin, 100 college students were randomly selected. What is the probability that the mean number of hours spent playing video games is less than 21.8 hours? Use the z-table below. Round your answer to three decimal places if necessary. z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -1.3 0.097 0.095 0.093 0.092 0.090 0.089 0.087 0.085 0.084 0.082 -1.2 0.115 0.113 0.111 0.109 0.107 0.106 0.104 0.102 0.100 0.099 -1.1 0.136 0.133 0.131 0.129 0.127 0.125 0.123 0.121 0.119 0.117 -1.0 0.159 0.156 0.154 0.152 0.149 0.147 0.145 0.142 0.140 0.138 -0.9 0.184 0.181 0.179 0.176 0.174 0.171 0.169 0.166 0.164 0.161 -0.8 0.212 0.209 0.206 0.203 0.201 0.198 0.195 0.192 0.189 0.187

Answer 1

The probability that the mean number of hours college students spent playing video games is less than 21.8 hours is 0.159, based on a z-score calculation using the given sample size and population standard deviation.

Step-by-step explanation:

The student is asking about the probability that the mean number of hours college students spent playing video games is less than 21.8 hours given that the population mean is 22 hours with a population standard deviation of 2 hours.

First, we need to find the z-score which requires the formula z = (X - μ) / (σ / √N), where X is the sample mean, μ is the population mean, σ is the population standard deviation, and N is the sample size.

Using the information provided:

• Sample Mean (X) = 21.8
• Population Mean (μ) = 22
• Population Standard Deviation (σ) = 2
• Sample Size (N) = 100

We find the z-score as follows:

z = (21.8 - 22) / (2 / √100) = (21.8 - 22) / (2 / 10) = -0.2 / 0.2 = -1

Consulting the provided z-table, a z-score of -1 correlates to a probability of 0.159. Therefore, the probability that the mean number of hours spent playing video games is less than 21.8 hours is 0.159, or when rounded, 0.159.