Statistics and Probability Answers

1. Serah needs access to Academia’s historical records. She must input a 5 digit code to access the
computer. Please find the following. Keep you solutions exact to four decimal places if needed.
(a) Calculate the Sample Space
(b) What is the probability the code contains no repeats?
(c) What is the probability the code ends with an even number?
(d) What is the probability the code contains only odd numbers?
(e) What is the probability the code ends with 2?

Find the probability that 5 students seek assistance in a month

True / False: A randomization test for H0 : p1 = p2 uses a randomization distribution centered at 0.

There 8 finalists in a 100-meter race competition. In how many ways can gold, silver, and bronze medals be awarded?

The use of online meeting tools has exploded due to an increase in remote workers from COVID-19. Information on types of online meeting tools and their duration has been gathered and your assistance is required. Which one of the following statements is incorrect with regard to types of variables

In a club with 9 male and 12 female​ members, a ​6 -member committee will be randomly chosen. Find the probability that the committee contains at least 5 women.

An automobile association offers its members a towing service. For a monthly fee of $15 it will provide unlimited towing for free in case of a breakdown. Based on past data there is a 2 in 100 chance that a member will need one tow in a month; there is a 3 in 500 chance that a member will need two tows in a month, and no member ever needs more than 2 tows in a month. Suppose it costs the association $140 to provide one tow. Let Y the association’s net monthly revenue (profit) from each member who enrolls in the program.
Provide a probability distribution table for Y

Sara downloaded a game on her phone. The objective of this game is to face obstacles with the help of characters which can be of three types: "Earth", "Air" or "Fire".

At the start of each game, Sara randomly obtains the character of one of the three types and may, during the game, keep that character or change the character type only once.

We consider Sara played 10 rounds, taken independently of each other.

The probability that she will get an “Earth” type character is 0.3.

Y designates the random variable which counts the number of characters of type “Earth” obtained at the beginning of the round.

1. Justify that this situation can be modeled by a binomial distribution, where you specify its parameters.

2. Calculate the probability that Sara obtains exactly 3 “Earth” -type characters.

3. Calculate the probability that Sara obtains at least once an “Earth” type character at the start of his games.

If r 12 =0.7, r 23 =r 31 =0.6, find the partial correlation coefficient between x 1
and x 2 keeping x 3 as constant. Find the multiple correlation coefficient
R 1.23