Probability and Statistics

A mechanic serviced the following number of vehicles over a five-day period: $10$, $15$, $4$, $11$, and $5$.

What is the median number of vehicles serviced during this period?

During a land navigation exercise, an instructor maps out 150 possible waypoint coordinates. Of these waypoints, 45 are located in dense forest, 35 are in open terrain, 50 are near water features, and the remaining waypoints are on elevated ridges. If a cadet is randomly assigned one waypoint coordinate, what is the probability that it is located on an elevated ridge? (Express your answer as a simplified fraction)

An aviation squadron has a total of $30$ crew members available for assignment. The squadron consists of $12$ pilots, $10$ mechanics, $5$ medics, and $3$ navigators. If one crew member is randomly selected to lead a safety briefing, what is the probability that the selected member is NOT a mechanic?

A quality control inspector records the weight variations, in ounces, of five identical manufactured parts. The recorded weights are: $8.5$, $4.0$, $10.5$, $6.0$, and $7.5$. What is the range of these recorded weights?

An armory has a total of $50$ training rifles on a rack. Exactly $15$ of these rifles are equipped with laser sights. If a recruit is randomly issued one of these training rifles, what is the probability, expressed as a decimal, that they receive a rifle with a laser sight?

A deck of flashcards used for language training contains $50$ cards. There are $15$ vocabulary cards, $25$ grammar cards, and $10$ phrase cards. If a student randomly selects one card from the deck to study, what is the probability that it is a vocabulary card?

Match each statistical request with its correct numerical value based on the provided data sets.

A student recorded the number of books they read each month over a five-month period: $12$, $7$, $19$, $4$, and $13$. What is the median number of books read per month?

A logistics manager is tracking the number of supply crates shipped each week. Over the first four weeks of a five-week period, the facility shipped $13$, $27$, $18$, and $26$ crates. How many crates must be shipped in the fifth week to achieve an average (mean) of $24$ crates per week for the entire five-week period?

A logistics officer is analyzing the fuel consumption of five transport trucks. The data for the first four trucks is $45$, $52$, $48$, and $55$ gallons. The fuel data for the fifth truck was lost, but the officer remembers that it consumed more fuel than any of the other four trucks. If the mean fuel consumption of all five trucks is exactly equal to their median, how many gallons of fuel did the fifth truck consume?

A logistics specialist is inventorying six shipping crates. The median weight of the crates is $45$ pounds, and the mode is $40$ pounds. The weights of five of the crates are $50$, $40$, $55$, $42$, and $40$ pounds. What is the weight of the sixth crate?

Review the four distinct practical situations below. Pair each descriptive problem with its mathematically correct calculated result.

Match each statistical scenario with its corresponding numerical value based on the principles of central tendency.

A naval navigation team is evaluating different telemetry datasets. Match each statistical description to its correct calculated value.

A culinary instructor is reviewing the final exam scores of six students to determine the middle performance level of the class. The scores recorded are $84$, $72$, $90$, $76$, $88$, and $64$. What is the median score of this group of students?

A quality control inspector is reviewing a batch of 12 electronic components, of which 8 are functioning properly and 4 are defective. If the inspector randomly selects 3 components from the batch one at a time without replacement, what is the probability that exactly 2 of the selected components are functioning properly and 1 is defective?

A maintenance chief is reviewing the repair times (in hours) for five generators: $8$, $12$, $15$, $9$, and $16$. A sixth generator's repair time is added to the records. If the median repair time for all six generators is exactly $11.5$ hours, what is the repair time of the sixth generator?

A cybersecurity analyst is monitoring the number of unauthorized access attempts blocked by a firewall each day. The mean number of blocked attempts for the entire $5$-day work week is exactly $32$. If the daily counts from Monday to Thursday were $28$, $35$, $27$, and $34$, how many access attempts were blocked on Friday?

A medical detachment is tracking a patient's resting heart rate over a six-day period. The mean heart rate over the six days is $69$ beats per minute (bpm). The readings for five of those days are $66$, $72$, $68$, $78$, and $65$. What is the median heart rate for the entire six-day period?

An environmental scientist measures the daily water flow (in gallons per minute) from a natural spring over five days. The recorded values are $22$, $18$, $25$, $20$, and $17$. If the scientist needs the average (mean) flow rate across a full six-day period to be exactly $21$ gallons per minute, what must the flow rate be on the sixth day?