For the experiment described below, let x determine a random variable, and use your knowledge of probability to prepare a probability distribution. Three balls are drawn (without replacement) from a bag that contains 5 red balls and 6 blue balls. The number of blue balls is counted. A probability distribution for the given experiment is as follows. x 0 1 2 3 P(x) (Type simplified fractions.)

A small inn has 4 rooms.  Let X represent the number of rooms that are rented out on any given Saturday. The following table describes the probability distribution of X.     What is the mean of the random variable X?   μX =

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Can you please help me solve these 2 questions?

Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).t Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and a- 0.90 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is u= 4.70 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.70 grams? Use a- 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? Ho: H 4.7 g; right-tailed Ho: H= 4.7 g; H: < 4.7 g; left-tailed Ho: H- 4.7 g; H: 4.7 g; two-tailed (b) What sampling distribution will you use? Explain the rationale…

Here is the probability model for the blood type of a randomly chosen person in the United States. Blood type O A B AB Probability 0.53 0.22 0.06 0.19 What is the probability that a randomly chosen American does not have type O blood? ______________% Round to the nearest 0.01%

Pedro has a box that contains various numbers of wooden shapes. He randomly draws out a shape and then places it back in the box. He repeats this process for a total of 36 times. The table shows his data. Experimental Data for Shapes Number of Times Shape Drawn Out Sphere Cube 6. 4 Square pyramid Triangular prism 12 14 Based on the data, what is the probability that the next shape he draws from the box is a square pyramid? 2/9

Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).t Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and o = 0.96 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is µ = 4.80 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.80 grams? Use a = 0.10. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right- tailed, or two-tailed test? O Ho: H 4.8 g; right-tailed O Ho: H = 4.8 g; H1: µ < 4.8 g; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of…

The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children.  a. Find the probability of getting exactly 6 girls in 8 births. b. Find the probability of getting 6 or fewer girls in 8 births.