In Chapter 9 question 37 for the Sampling distribution of a proportion. The manager of a restaurant in a commercial building has determined that the proportion of customers who drink tea is 14%, What is the probability the in the next 100 customers at least 10% will be tea drinkers? I increased my sample size to 200 and 400 and my number got closer to 1. What am I doing wrong?

An urn contains five black marbles and one orange marbles. Four marbles are drawn out one at a time. For each marble, if it is black the marble is set aside, but if it is orange it is returned to the urn before the next marble is drawn. Let X be the number of black marbles drawn from the urn. Find the probability distribution for X and find the expectation value and variance of X

You roll a​ die, winning nothing if the number of spots is

eveneven​,

​$77

for a

11

or a

33​,

and

​$1616

for a

55.

​a) Find the expected value and standard deviation of your prospective winnings.

​b) You play

three timesthree times.

Find the mean and standard deviation of your total winnings.

​c) You play

3030

times. What is the probability that you win at least

​$190190​?

A company has 3 machines: A, B, and C. The number of breakdowns per week is distributed Poisson. On average, machine A breaks down .4 times per week, machine B breaks down .45 times per week and machine C breaks down .9 times per week. The probability that there are 2 breakdowns in one week is _____ (round to 4 decimal places).

The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 4639 4639 miles, with a standard deviation of 437 437 miles. If he is correct, what is the probability that the mean of a sample of 32 32 cars would differ from the population mean by less than 181 181 miles? Round your answer to four decimal places.

Bob is an amoeba that behaves as follows: at the end of any given minute, Bob either splits into two identical and independent copies of himself, stays the same without splitting, or dies; all three of these happen with equal probability. All subsequent Bobs behave identically and independently to the original Bob. If there is only 1 Bob at the start, find the expected number of Bobs after 2 minutes

Use Excel to answer. A college admission officer for an MBA program determines that historically candidates have undergraduate grade averages that are normally distributed with standard deviation of .45. A random sample of 25 applications from the current year yields a sample mean grade point average of 2.90.

1. Find a 95% confidence interval for the population mean, μ. (Round the boundaries to 2 decimal places.)

2. Based on the same sample results, a statistician computes a confidence interval for the population mean as 2.81< μ < 2.99. Find the α for this interval and the probability content (1- α) as well. (Round to 4 digits.) (Note: the correct α is a higher number than traditional α used; so don’t worry if your number “looks” wrong!)

Hint: first calculate α/2 using either the lower bound (2.81) or upper bound (2.99); then calculate α. Finally, calculate the probability content of the interval, which is (1- α). And make sure you use the standard error, not the standard deviation, to calculate α/2.

One of the scenarios below is a Binomial Experiment and the other is not. For each​ scenario, state whether or not it is a Binomial Experiment. If it​ is, give the values of n and p and state all the possible values of X. If it is​ not, say why​ (which of the four conditions are not​ met?).

​(a) In the 2008 presidential​ election, 54% of the voters voted for President Obama. Suppose 5 people who voted in the 2008 election are randomly selcted. The random variable represents the number of people in the random sample who voted for President Obama in the 2008 election.

​(b) Suppose that the probability that a randomly selected person who has recently married for the first time will be divorced within 5 years is​ 0.2, and that the probability that a randomly selected person who has recently married for the second time is 0.3. We take a random sample of 20 people who recently married​ (10 for the first time and 10 for the​ second). The sample is chosen so that no one in the sample is married to anyone else in the sample. The

random variable represents the number of people in the sample of 20 who will be divorced within 5 years.

A food researcher claims that there is a difference in the number of calories contained in sandwiches purchased from Deli A and Deli B. The researcher purchased 10 sandwiches from Deli A, and 10 from Deli B, and recorded the number of calories for each sandwich as follows:

a) What is the test statistic? A. -1.058 B. 1.058 C. Either A or B

b) Is the hypothesis test used to compare the calories in sandwiches from Deli A to that from Deli B

   A. left-tailed B. right-tailed C. two-tailed

c) The probability value for the event in which the test statistic is as high as (or as low as) the value calculated in part a is:

   A. 0.029 B. 0.145 C. 0.290

d) Comparing the probability value (calculated in part a) with a level of significance of 0.05, it can be stated that:

   A. There is enough evidence to reject the researcher's claim

   B. There is not enough evidence to reject the researcher's claim

   C. There is enough evidence to support the researcher's claim

Joe Hammer is thinking about setting up a special counter for the do-it-yourself customers at which they can get, not only help where to find products in the store, but also some quick advice about the best way to handle their upcoming projects. Experience has taught Joe that six minutes is a good figure to allow for the average time required to serve a “do-it-yourselfer” and that these customers will arrive every 15 minutes throughout the day.

a.) If joe sets up the counter under these conditions, what operating characteristics might he expect?

b.) What might Joe do to avoid the costs of idleness?

c.) What is the likelihood(probability) that three or more customers will be at the counter, either waiting or being served, at any given time?

Calculate the Utilization rate, idleness rate, Average time in queue, Average time in system, Average number in queue, Average number in system, and probability that three or more customers will be in the counter system at the same time. Can you please show calculation for P_0, p_1, p₂, p₃ please.