The table below shows the distribution of calls handled per shift by a group of $100$ call centre agents surveyed on a working day in Manila.

A agent is chosen at random from the group of $100$ agents.

A second agent is chosen at random from the group of $100$ agents.

The length of breaks taken by the $100$ agents was normally distributed with a mean of $10$ minutes and a standard deviation of $2.5$ minutes.

The $100$ agents were selected for the survey by dividing the full workforce into three shift groups and randomly choosing a fixed number from each shift group.

The lifetimes $T$, in hours, of rechargeable batteries follow a normal distribution $T\sim \text{N}(\mu ,{\sigma }^2)$. A battery is labeled as unreliable if it lasts less than 18 hours. To reduce the proportion of unreliable batteries, the manufacturer sets the probability of an unreliable battery to 0.005. They decide to increase the mean $\mu$ while keeping the standard deviation $\sigma$ constant. The previous adjustment is found unsatisfactory, so the manufacturer sets the mean $\mu$ back to 22 and instead decreases $\sigma$ to maintain the 0.005 probability threshold.

The table below shows the distribution of patients attended per shift by a group of $100$ nurses surveyed on a working day in Dublin.

A nurse is chosen at random from the group of $100$ nurses.

A second nurse is chosen at random from the group of $100$ nurses.

The time spent with each patient by the $100$ nurses was normally distributed with a mean of $12$ minutes and a standard deviation of $2.5$ minutes.

The $100$ nurses were selected for the survey by ensuring $25$ nurses from each of the hospital's $4$ departments were chosen at random.

A florist prepares bouquet orders for a hotel. The time, $F$ minutes, needed to prepare an order for collection follows a normal distribution $F\sim \text{N}\left(18,5^2\right)$. Lina starts preparing an order at 13:10. The first courier pickup is at 13:30. The delivery time, $D$ minutes, is normally distributed with $D\sim \text{N}\left(28,{\sigma }^2\right)$. The probability that the delivery takes less than $34$ minutes is $0.9332$. If the first pickup is missed, a second pickup is at 13:45. The order must arrive at the hotel by 14:05 to be on time. If both pickups are missed, the order is late. $F$ and $D$ are independent.

At a publishing house, the probability, $P(C)$, that all article proofs are corrected before noon is 0.64. The probability, $P(M)$, that the magazine is sent to print on time is 0.71. The probability that both events occur is 0.39. The number of pages proofread last week by copy editors follows a normal distribution with mean 140 pages and standard deviation $\sigma$. It is observed that 97.72% of copy editors proofread fewer than 220 pages last week. Assume the numbers for different copy editors are independent.