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A petrol pump station has two pumps. The
service times follows the exponential
distribution with a mean of 4 minutes and
cars arrive for service in a Poisson process at
the rate 10 cars per hour. Find the
probability of that a customer has to wait for
service.
Raphael’s grades in his statistics classes are as follows: Quizzes: 62, 88, 82 Laboratories: 89, 96 Examinations: 87, 99 a. In this class, quizzes count once, laboratories count twice as much as a quiz, and examinations count three times as much as a quiz. Determine the mode, mean and median. b. If Raphael’s quiz grade of 62 was removed from the data, briefly describe the anticipated effect on the statistics you calculated in part (a).
A jar contains 5 red marbles, 5 white marbles, and 6 blue marbles. Two marbles are randomly selected from the jar with replacement. Find the following probabilities. Leave your answer as a reduced fraction.
A family has four children. If x is a random variable that pertains to the number of female children, what are the possible values of x
Let x be a random variable that denotes the number of passenger in a train station for a given hour. What are the possible values of x
It is known from the records of the city schools that the standard deviation of mathematics test score on the XYZ test is 5. A sample of 200 pupils were taken and it was found that the sample mean score is 75. Previous tests showed the population mean to be 70. Is it safe to conclude that the sample is significantly different from the population at 5% significance level?
Sally has 11 pairs of socks in her drawer. Each pair is a different color and design, but they are not together as pairs; they are just in her drawer scattered about. With her left hand, Sally reaches in and picks one sock.
a. While holding that one sock in her left hand, Sally reaches into the drawer and picks another
sock. What is the probability of her getting a sock that will match the sock in her left hand?
Vector A=2ti+tj-t^3k and B=sinti+costj evaluate
A..d/dt(A.B)
B..d/dt(A.A)
C..d/dt(A×B)
D..show that d/dt(A×A) is equal to zero.
An experimental study was conducted by a researcher to determine if a new time slot has an effect on the performance of pupils in mathematics. Fifteen randomly selected learners participated in the study. Toward the end of the investigation, a standardized assessment was conducted. The sample mean was 𝑿̅ = 𝟖𝟓 and the standard deviation s = 3. in the standardization of the test, the mean was 75 and the standard deviation was 10. based on the evidence at hand, is the new timeslot effective?
In a betting game wherein the result may be one of the following in one turn: break even, win 5 peso or lose 3 peso. How much will be the amount a player gets after three turns. Let X be the total amount of a player gets after three turns.
