Browsing as Guest. Progress, bookmarks and attempts are disabled.
Log in to track your work.
Nov 2021 p51 q7
3186
The times, in minutes, that Karli spends each day on social media are normally distributed with mean 125 and standard deviation 24.
On 90% of days, Karli spends more than t minutes on social media.
Find the value of t.
Solution
We are given that the times are normally distributed with mean \(\mu = 125\) and standard deviation \(\sigma = 24\). We need to find the value of \(t\) such that 90% of the time, Karli spends more than \(t\) minutes on social media.
This implies that 10% of the time, Karli spends less than \(t\) minutes. We need to find the z-score corresponding to the 10th percentile of the standard normal distribution, which is \(z = -1.282\).
Using the standardization formula:
\(z = \frac{t - \mu}{\sigma}\)
Substitute the known values:
\(-1.282 = \frac{t - 125}{24}\)
Solving for \(t\):
\(t - 125 = -1.282 \times 24\)
\(t - 125 = -30.168\)
\(t = 125 - 30.168\)
\(t = 94.832\)
Rounding to one decimal place, \(t \approx 94.2\).