Question

1. the daily viewing times for a popular video streaming platform are normally distributed, with a mean of 62 minutes and a standard deviation of 11 minutes. if drew spends 65 minutes per day using this platform, approximately what percentage of users spend less time per day than drew using this platform?

a. 27%
b. 38%
c. 62%
d. 73%
e. 3%

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value of interest, $\mu$ is the mean, and $\sigma$ is the standard deviation. Given $\mu = 62$, $\sigma=11$, and $x = 65$. Then $z=\frac{65 - 62}{11}=\frac{3}{11}\approx0.27$.

Step2: Use the standard normal table

We want to find $P(X<65)$, which is equivalent to $P(Z < 0.27)$ when $X$ is normally distributed with mean $\mu$ and standard deviation $\sigma$ and $Z=\frac{X-\mu}{\sigma}$. Looking up the value of $P(Z < 0.27)$ in the standard - normal table (the cumulative distribution function of the standard normal distribution), we find that $P(Z < 0.27)\approx0.6064\approx62\%$.

Answer:

C. 62%