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Of the trains that recently arrived at Hampton Station, 4 were on time and 2 were late. Considering this data, how many of the next 12 trains would you expect to be on time?
? trains

Consider a Poisson distribution with a mean of two occurrences per time period.
What is the expected number of occurrences in three time periods?

An engineering company has four openings and the applicant pool consists of 6 database administrators and eight network engineers. All are equally qualified so the hiring will be done randomly. The hiring committee consists of 4 women and 4 men.
d. How many ways can 1 network engineers be chosen?
e. What is the probability that the random selection of the four persons to be hired will result in 3 database administrators and 1 network engineer?

Suppose you are a fan of baseball, which has two different leagues in the US, the National League and the American League. The winners of both the leagues play in the World Series Championship each year. You want to test whether both the leagues are equally strong, or whether one of the leagues is stronger than the other. Assume that each year the AL champion wins the world series with probability p, and the NL champions win with probability ${\displaystyle 1-p}$, where p is an unknown number in (0, 1).
Starting from 1903, the world series championship has been played 115 times, and the AL champions won it 66 times, and the NL champions won it 49 times. Based on this data, carry out the following tests of hypothesis:
(a) ${\displaystyle H_0:p=\frac{1}{2}versus{H}_1:p>\frac{1}{2}at\le vel\alpha =.1}$.
(b) ${\displaystyle H_0:p=\frac{1}{2}versus{H}_1:p\ne \frac{1}{2}at\le vel\alpha =.1}$.

Five hundred people were chosen at random from a large population and each was asked whether he or she favoured capital punishment for murderers of police officers. Suppose that 60% of those interviewed said that they were in favour. Let ${\displaystyle \theta }$ denote the proportion of the population who are in favour. Construct a 95% confidence interval for${\displaystyle \theta }$ from the observed data.

Use linear regression to find the equation for the linear function that best fits this data. Click Read Button For online regression calculator. Round both numbers to two decimal places. Write your final answer in a form of an equation ${\displaystyle y=mx+by=mx+b}$
$$\begin{array}{|ccccccc|}\hline x& 1& 2& 3& 4& 5& 6\\ y& 74& 90& 109& 123& 143& 155\\ \hline\end{array}$$

From a classroom of 23 students, the number of students taking Data Management is 13, the number taking Calculus is 9. There are 5 students who are not taking either course.
How many students are taking just Data Management?

The following data represents the number of home runs that Ryan Howard, a major league baseball player for the Philadelphia, hit over a six-year period.
22 58 47 48 45 31
what is the median for this data set?

Suppose, household color TVs are replaced at an average age of ${\displaystyle \mu =8.2years}$ after purchase, and the (95% of data) range was from 6.2 to 10.2 years. Thus, the range was ${\displaystyle 10.2-6.2=4.0}$ years. Let x be the age (in years) at which a color TV is replaced. Assume that x has a distribution that is approximately normal.
(a) The empirical rule indicates that for a symmetrical and bell-shaped distribution, approximately 95% of the data lies within two standard deviations of the mean. Therefore, a 95% range of data values extending from ${\displaystyle \mu -2\sigma \to \mu +2\sigma }$ is often used for "commonly occurring" data values. Note that the interval from ${\displaystyle \mu –2\sigma \to \mu +2\sigma is4\sigma }$ in length. This leads to a "rule of thumb" for estimating the standard deviation from a 95% range of data values.Estimating the standard deviation
For a symmetric, bell-shaped distribution,
${\displaystyle \text{standard deviation}\approx ran\ge 4\approx \text{high value}-\text{low value}}$
where it is estimated that about 95% of the commonly occurring data values fall into this range. Use this "rule of thumb" to approximate the standard deviation of x values, where x is the age (in years) at which a color TV is replaced. (Round your answer to one decimal place.)
(b) What is the probability that someone will keep a color TV more than 5 years before replacement? (Round your answer to four decimal places.)
(c) What is the probability that someone will keep a color TV fewer than 10 years before replacement? (Round your answer to four decimal places.)

Calculate the Mean, Median and Modal numbers of persons per house from the data:
$$\begin{array}{|ccccccccccc|}\hline \text{No. of persons per house}& 1& 2& 3& 4& 5& 6& 7& 8& 9& 10\\ \text{No. of houses}& 26& 113& 120& 95& 60& 42& 21& 14& 5& 4\\ \hline\end{array}$$

Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row of 5 seats, one person per seat. In how many of those ways is Martha sitting in the middle seat?

The following are prices of a sanitizer sold at a few selected stores in a District A during the COVID-19 pandemic. Based on the sample data, at 0.05 level of significance, can we conclude the average price of the sanitizer in District A is RM10.50? Make your conclusion using the p-value approach, with the aid of Mic. Office EXCEL.
RM10.00,RM11.50,RM9.70,RM11.20,RM10.70,RM10.20,RM9.70

Consider a Poisson distribution with a mean of two occurrences per time period.
Compute the probability of two occurrences in one time period.

A study tested the claim that heights of Americans and heights of Austrians have different variances with ${\displaystyle s=7.48092}$ cm for Americans and 7.14756 cm for Austrians. The sample sizes are ${\displaystyle n1=145\text{and}n2=157}$. When using the F test with these data, is it correct to reason that there is no need to check for normalcy because n1 is greater than 30, and n2 is greater than 30?

The amount of chlorine in 100 cm3 water taken from a water tank was measured, the average was 2.15 mg was found. The expert claims that the amount of chlorine in the water is greater than that measured. For this reason, 100 households were randomly selected, with an average chlorine content of 2.55mg and a variance of 0.49 mg. According to this data, find the account value z.

Consider the following data set.
The annual wages of employees at a small accounting firm are given in thousands of dollars.
25 25 30 30 35 35 50 60 16 14 18 18 20
Prepare a frequency distribution for the data set.
$$\begin{array}{|cc|}\hline Wages& Frequency\\ 14\\ 16\\ 18\\ 20\\ 25\\ 30\\ 35\\ 50\\ 60\\ \hline\end{array}$$

An insurance policy sells for $1,000. Based on your past data, an average of 1 in 50 policyholders will file a $9,000 claim, an average of 1 in 100 policyholders will file a $24,000 claim, and an average of 1 in 250 policyholders will file a $55,000 claim. Find the expected value for the company per policy sold.