Statistics and Probability Answers

You want to impress your family and you are wondering if you could find a farm where you could be sure to get very big pumpkins, like 25 pounds on average. A friend shows you the 4 pumpkins she got at the SuperPumpkins Farm, and you are able to calculate that the mean weight of this sample of 4 pumpkins to be 27 pounds. To find out the true population mean weight at the SuperPumpkins Farm, you decide to build a 99% confidence interval with this sample data from your friend, assuming that the population standard deviation should be 6 pounds (i.e. typical for pumpkins, the same as the Huckleberry Farm). Based on this confidence interval you built, do you feel confident that the SuperPumpkins Farm will have very big pumpkin of around 25 pounds on average. round to 2 decimals, !

In a study of the domestic market share of three major automobile manufacturers A, B and C in a certain country, it was found out that of the customers who bought a car manufactured by A, 75% would again buy a car manufactured by A, 15% would buy a car manufactured by B and the rest would buy a car manufactured by C. Of the customers who bought a car manufactured by B, 90% would again buy a car manufactured by B, 5% would buy a car manufactured by A and the rest would buy a car manufactured by C. Of the customers who bought a car manufactured by C, 85% would again buy a car manufactured by C, 5% would buy a car manufactured by A and the rest would buy a car manufactured by B.Required
The long run market share of the manufacturers

While buying a bicycle, Kylie can choose between three materials
(wood, steel, and carbon fiber), between a digital and an analog
gauge, and between 15 different tire brands.
How many combinations are there in total?

Three types of vitamins, five types of minerals, and sixteen types of
artificial flavors are available to prepare a snack.
If only 1 vitamin, 1 mineral, and 1 flavor can be added,
how many combinations are there?

Today, Hal has three assignments with six questions each. If
each question has two sub-parts, in how many ways can Hal
complete the assigned work?

Megan can wear a blue, black, or red dress to one of the 5
parties she is invited to. How many combinations are there if
she can bring one of the 9 drinks to the selected party

The captain makes a team of one boy and one girl.
How many combinations are there if there
are 9 boys and 8 girls in the class?

The table below displays results from experiments with polygraph instruments. Find the positive predictive value for the test. That​ is, find the probability that the subject​ lied, given that the test yields a positive result.

Did the Subject Actually​ Lie?
No​ (Did Not​ Lie) Yes​ (Lied)
Positive test results 20 40
Negative test results 32 11

The probability is (Round to 3 decimals)

(4.3.23) Testing for a disease can be made more efficient by combining samples. If the samples from five people are combined and the mixture tests​ negative, then all five samples are negative. On the other​ hand, one positive sample will always test​ positive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is0.2 ​, find the probability of a positive result for five samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely​ necessary?
The probability of a positive test result is ?(Round to 3 decimals places)