Give an event in the context of the problem whose probability can be calculated using the term $\left( \frac { 3 } { 4 } \right) ^ { 5 }$, and justify your answer.
Determine the probabilities of the following events:\ $D$ : ``Among the selected cars there are seven or eight combustion engine cars with diesel motors.''\ $E$ : ``Among the selected cars there are more than 135 with purely electric drive.''
QB 1b
3 marksHypothesis test of binomial distributionsView
Give an event in the context of the problem whose probability can be calculated using the term $\sum _ { k = 0 } ^ { 25 } \binom { 200 } { k } \cdot 0,1 ^ { k } \cdot ( 1 - 0,1 ) ^ { 200 - k }$.
The random variable $X$ describes the number of cars with electric motors among the selected vehicles. Calculate the expected value and the standard deviation of $X$.
For a certain value $n \in \{ 1 ; 2 ; 3 ; \ldots \}$, the binomially distributed random variables $Z _ { p }$ with parameters $n$ and $p$ are considered for $p \in ] 0 ; 1 [$. Show that among these random variables, the one with $p = 0.5$ has the greatest variance.
From the newly registered cars with electric motors, 40 vehicles are randomly selected. Determine the probability that exactly ten plug-in hybrids are among them.
At the beginning of 2021 in Germany, approximately 320000 cars with purely electric drive and 280000 plug-in hybrids were registered, thus a total of approximately 600000 cars with electric motors. The share of cars with electric motors in the total stock of all cars registered in Germany was around $1.2 \%$. Determine the number of cars that must be randomly selected from this total stock so that with a probability of more than $97 \%$ at least one car with purely electric drive is among them.
Determine, assuming that the proportion of employees with a job ticket is the same at both locations, the probability that a randomly selected employee of the automotive supplier works at location B and does not have a job ticket.
In fact, the proportion of employees with a job ticket is different at the two locations; at location B, only half of the employees have a job ticket. Calculate the probability that a randomly selected employee of the automotive supplier who has a job ticket works at location A.