Statistics and Probability Answers

A random variable X is distributed normally with E(X) = 8 and σ(X) =3 . Find P(9≤X<11).

X_1,X_2,… X_121 are independent and identically distributed random variables such that E(X_i ) = 3 and Var (X_i ) = 25. What is the standard deviation of their average? In other words, what is the standard deviation of X = (X_1 + X_2 + … + X_121) / 121?

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 13 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 5% rate of defects, what is the probability that this whole shipment will be accepted?

Let a fair die be rolled 2 times. Let’s assume that the 2 rolls are independent. Let X and Y be the outcomes of the first and second rolls, respectively.
a. What is the probability distribution of X+Y? That is, create a table that contains each unique possible value of X+Y (each value only listed once) and each possibility’s corresponding probability.
b. What is the probability that X+Y is greater or equal to 10?

We have a fair eight-sided die.

a. Find the math expectation of a single roll.

b. Find the math expectation of the numerical sum of 4 rolls.

c. Find the math expectation of the numerical product (i.e., multiplication) of 5 rolls.

In certain countries 43.8% of 3year olds are enrolled in daycare. what is the probability that randomly selected 3year old is enrolled in daycare

If the cumulative distribution function of X is given by the function below, then what is P (X < 0.80).
f(x) = 0 , if x ≤ 0
f(x) = x^2, if 0 < x ≤ 1
f(x) = 1 , if x > 1

Your DNA code is composed of a series of four nucleotides: adenine, guanine, thymidine and cytosine (A, G, T and C, respectively).

1) What is the probability an individual has the following nucleotide sequence: “TATATA” at any particular position? (assuming independence).

2) What is the probability that an individual has k T’s in their DNA code at any particular position? (k can be any integer and you may assume independence). Here we're looking for the probability of k consecutive T's.

Professor Karl has n students in her classroom. At the end of the semester she decides to assign the students a group final project. If Professor Karl wants the students to pair into groups of 3, how many ways are there to choose the groups in which the order doesn’t matter (the group Mike, John and Matt is the same as the group Matt, Mike and John).

Express the indicated degree of likelihood as a probability value. "Your mother could not have died two years before you were born."
A. 0.25
B. 0
C. 0.5
D. 1