Statistics - math word problems

Father and sons
Father is 27 and his sons 2 and one year. In how many years will his sons sum up to half his age?
Before yesterday
He merchant adds a sale sign in his shop window to the showed pair of shoes in the morning: "Today by p% cheaper than yesterday. " After a while, however, he decided that the sign saying: "Today 62.5% cheaper than the day before yesterday". Determine the
AM of three numbers
The number 2010 can be written as the sum of 3 consecutive natural numbers. Determine the arithmetic mean of these numbers.
Frustum of a cone
A reservoir contains 28.54 m³ of water when completely full. The diameter of the upper base is 3.5 m while at the lower base is 2.5 m. Determine the height if the reservoir is in the form of a frustum of a right circular cone.
The escalator
I run up the escalator at a constant speed in the direction of the stairs and write down the number of steps A we climbed. Then we turn around and run it at the same constant speed in the opposite direction and write down the number of steps B that I clim
In center
What number lies in the center between a quarter of a fifth and a half of a third on the number axis?
The sum
The sum of the first 10 members of the arithmetic sequence is 120. What will be the sum if the difference is reduced by 2?
Holidaymakers
A total of 94270 holidaymakers spent part of their holiday in 50 hotels a year. On average, how many vacationers are there for one hotel?
Between two bus stops
Wanda lives between two bus stops at three-eighths of their distance. He started the house today and found that whether he was running to one or the other stop, he would have arrived at the bus stop. The average bus speed is 60 km/h. What is the average
Positive integers
Several positive integers are written on the paper. Michaella only remembered that each number was half the sum of all the other numbers. How many numbers could be written on paper?
Average speed
The truck drove 1/2 of the way on the highway at 80km/h. The other half of the way 20km/h. Calculate the average speed
Records
Records indicate 90% error-free. If 8 records are randomly selected, what is the probability that at least 2 records have no errors?
Genetic disease
One genetic disease was tested positive in both parents of one family. It has been known that any child in this family has a 25% risk of inheriting the disease. A family has 3 children. What is the probability of this family having one child who inherited
Probability of malaria
A survey carried out at a certain hospital indicates that the probability that a patient tested positive for malaria is 0.6. What is the probability that two patients selected at random (i) one is negative while the other tested positive? (i) both patie
Three altitudes
A triangle with altitudes 4; 5 and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle.
Life expectancy
The life expectancy of batteries has a normal distribution with a mean of 350 minutes and standard deviation of 10 minutes. What the range in minutes 68% of the batteries will last? What is the range in minutes approximately 99.7% of batteries will last?
Here is
Here is a data set (n=117) that has been sorted. 10.4 12.2 14.3 15.3 17.1 17.8 18 18.6 19.1 19.9 19.9 20.3 20.6 20.7 20.7 21.2 21.3 22 22.1 22.3 22.8 23 23 23.1 23.5 24.1 24.1 24.4 24.5 24.8 24.9 25.4 25.4 25.5 25.7 25.9 26 26.1 26.2 26.7 26.8 27.5 27.
Sphere floating
Will float a hollow iron ball with an outer diameter d1 = 20cm and an inside diameter d2 = 19cm in the water? The iron density is 7.8 g/cm 3. (Instructions: Calculate the average sphere density and compare with the density of the water. )
Bonuses
Five employees of the company were paid bonuses so that each successor received a 550 USD less than the previous employee. How much did everyone get, if a total of USD 11,000 has paid?
Reading records
Lucy, Tereza, and Petra decided to compile the compulsory reading records together. It would take 30 days for Lucia alone, 36 for Tereza and 45 for Petra. How long will it take to make records if they will work together?