An agricultural research department planted a new type of rice on 100 rice paddies of equal area and obtained the yield per mu (unit: kg) for each paddy, with partial data organized in the table below

Yield per mu	[900, 950)	[950, 1000)	[1000, 1050)	[1100, 1150)	[1150, 1200)
Frequency	6	12	18	24	10

Based on the data in the table, the correct conclusion is
A. The median yield per mu of the 100 paddies is less than 1050 kg
B. The proportion of paddies with yield per mu below 1100 kg among the 100 paddies exceeds $80 \%$
C. The range of yield per mu of the 100 paddies is between 200 kg and 300 kg
D. The mean yield per mu of the 100 paddies is between 900 kg and 1000 kg

Determine the maximum possible value that the probability of $B$ can assume.
On a section of a lightly travelled country road, a maximum speed of 80 km/h is permitted. At one location on this section, the speed of passing cars is measured. In the following, only those journeys are considered where the drivers were able to choose their speed independently of one another.
For the first 200 recorded journeys, the following distribution was obtained after classification into speed classes: [Figure]
In 62\% of the 200 journeys, the driver was travelling alone, 65 of these solo drivers exceeded the speed limit. One journey is randomly selected from the 200 journeys. The following events are considered: $A$ : ``The driver was travelling alone.'' $S$ : ``The car was speeding.'' (1a) [5 marks] Show that events $A$ and $S$ are stochastically dependent, and give a possible reason for this in the context of the problem.
The speed measurements are continued over a longer period. It turns out that the distribution of speeds measured to the nearest km/h can be approximately described by a binomial distribution with parameters $n = 100$ and $p = 0.8$. For example, $B ( 100 ; 0.8 ; 77 )$ approximately corresponds to the proportion of cars recorded at a speed of $77 \mathrm {~km} / \mathrm { h }$.
(1b) [4 marks] Confirm by example for one of the two middle speed classes of the sample shown above that the determined number of journeys is consistent with the description by the binomial distribution.
(1c) [2 marks] Using this binomial distribution, determine the smallest speed $v ^ { * }$ for which the following statement holds: ``In more than 95\% of the recorded journeys, $v ^ { * }$ is not exceeded.''
The police conduct a speed check at the measurement location.
A speed of more than $83 \mathrm {~km} / \mathrm { h }$ constitutes a speeding violation. For simplicity, it should be assumed that the speed of a passing car is greater than $83 \mathrm {~km} / \mathrm { h }$ with a probability of 19\%.
(2a) [4 marks] Calculate the number of speed measurements that must be performed at minimum so that with a probability of more than 99\% at least one speeding violation is recorded.
(2b) [5 marks] If in a sample of 50 speed measurements the number of speeding violations is more than one standard deviation below the expected value, the police assume that there was effective warning of the speed check and abort the control. Determine the probability that the speed check is continued even though the probability of a speeding violation has dropped to 10\%.

If the mean of the frequency distribution

Class :	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency :	2	3	$x$	5

is 28, then its variance is $\_\_\_\_$.

Serkan's wardrobe contains three types of clothing: shirt ($G$), pants ($P$), and jacket (C). The numerical distribution of these clothes initially in the wardrobe is shown in the pie chart below.
Serkan takes a certain number of clothes from his wardrobe to dry cleaning. In the final situation, the numerical distribution of the clothes remaining in Serkan's wardrobe shown in the pie chart is the same as the initial one.
Given that Serkan initially had 5 jackets in his wardrobe and he took 1 of these jackets to dry cleaning, how many shirts are left in Serkan's wardrobe?
A) 8 B) 10 C) 15 D) 18 E) 20