Probability Distributions

Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n=70, p=0.4

Part 2 of 3 Points: 0 of 1 Save Let there be two players in a game, Player 1 and Player 2. Consider a jar containing 5 snakes. 3 of the snakes in the jar are venomous, while the remaining 2 are non-venomous. In the game, both the players have to put their hand in the jar one after the other and pick a snake out. Each snake, if picked out of the jar, will bite the player's hand. The event of picking a venomous snake, or equivalently, a venomous snake's bite will earn the player zero points. On the other hand, the event of picking a non-venomous snake, or equivalently, a non-venomous snake's bite will earn the player one point. Let $X$ denote Player 1 's pick and let $Y$ denote Player 2 's pick. Suppose Player 1 is the first to pick out a snake. The expected value of Player 1's pick is: $E(X)=0.4$. (Express your answer as a fraction or round your answer to two decimal places.) The expected value of Player 2's pick is: $E(Y)=$ (Express your answer as a fraction or round your answer to two decimal places.)

Given that a random variable X follows a normal distribution with a mean \( \mu = 15 \) and variance \( \sigma^2 = 25 \), find the standard deviation.

A random variable X follows a probability distribution with the probabilities P(X = 1) = 0.2, P(X = 2) = 0.3, P(X = 3) = 0.5. Find the variance of the distribution.

Using the Binomial distribution, If $n=5$ and $p=0.8$, find $P(x=5)$

Question Two hospitals send doctors to a medical conference. The first hospital sends 20 doctors, and the second hospital sends 30 doctors. Only 15 doctors will be given the chance to make presentations. What is the probability that exactly 8 of the doctors chosen to make presentations will be from the first hospital and exactly 7 of the doctors chosen to make presentations will be from the second hospital? Fill in the blanks for the answer below. Provide your answer below: FEEDBACK MORE INSTRUCTION SUBMIT

Use the range rule of thumb to identify significantly low or high values in the results: Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 14 . Complete parts (a) through (c) below. a. Find the mean and the standard deviation for the numbers of peas with green pods in the groups of 14 . The value of the mean is $\mu=10.5$ peas. (Type an integer or a decimal. Do not round.) The value of the standard deviation is $\sigma=1.6$ peas. (Round to one decimal place as needed.) b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. Values of peas or fewer are significantly low. (Round to one decimal place as needed.)