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Nov 2021 p51 q7
3115
The times, in minutes, that Karli spends each day on social media are normally distributed with mean 125 and standard deviation 24.
(i) On how many days of the year (365 days) would you expect Karli to spend more than 142 minutes on social media?
(ii) Find the probability that Karli spends more than 142 minutes on social media on fewer than 2 of 10 randomly chosen days.
Solution
(i) To find the number of days Karli spends more than 142 minutes on social media, we first calculate the probability that she spends more than 142 minutes on a given day. We use the standard normal distribution:
Using the standard normal distribution table, \(P(Z > 0.7083) = 1 - 0.7604 = 0.2396\).
Therefore, the expected number of days is \(0.2396 \times 365 = 87.454\).
Rounding to the nearest whole number, we get 87 or 88 days.
(ii) We need to find the probability that Karli spends more than 142 minutes on social media on fewer than 2 out of 10 days. This is a binomial probability problem with \(n = 10\) and \(p = 0.2396\).
