Data Distribution Questions and Answers

A company had it sales persons undergo training, hoping to improve their sales. Past sales data indicate that the average sale ewas P4,000 per transaction on a normally distrubuted population. After training, sales data, taken from a random sample of 25 salesmen/ salesladies, indicate and average sale of P4,500 with a standard deviation of P150.
(a) Write the null hypothesis.
(b) Write the alternative hypothesis.
(c) Formulate and calculate the test-statistic. Is it a one-tail or two-tailed test? Did the training work at 95% confindence level?

A child dying from an accidental poisoning is a terrible incident. Is it more likely that male child get into poison than a female child? To find this out, data was collected that showed that out of 1830 children between the ager and four who pass from poisoning, 1031 were males and 799 were females. Do the data show that there are more male children dying of poisoning than female children,Test at the 1% level?

The happiness score, by generation, conducted in a certain month is given in the following table (percent indicates the top-two box scores on a five-point happiness scale).
$$\begin{array}{|cccccc|}\hline \text{Generation}& Average18+& Millenials& GenerationX& Boomer& \text{Silent Genaration}\\ Score(\mathrm{\%})& 62.6& 58.1& 59.7& 65.0& 70.7\\ \hline\end{array}$$
Find the average happiness score for the five generations. ?%
What is the standard deviation for these data? (Round your answer to two decimal places.) ?%

Hamza comes to office located in Islamabad through different modes of transport. From his past data, it is known that the probability of him coming through car, bus, motobrike and rickshaw are respectively ${\displaystyle \frac{3}{10},\frac{1}{5},\frac{1}{10}\text{and}\frac{2}{5}}$. The probabilities that he will arrive to his office late are ${\displaystyle \frac{1}{4},\frac{1}{3},\text{and}\frac{1}{12}}$ if he comes by car, bus and motorbike. Interestingly, he will not be late if he comes by rickshaw. Suppose, he arrives late on Friday. What is the probability that he came by car?

The birthrates in the United States for the year 2003-2012 are given in the following table. (The birthrate is the number of live births/1000 population.)
$$\begin{array}{|cccccc|}\hline Year& 2003& 2004& 2005& 2006& 2007\\ Birthrate& 14.7& 14.0& 14.0& 14.2& 14.2\\ \hline\end{array}$$
$$\begin{array}{|cccccc|}\hline Year& 2008& 2009& 2010& 2011& 2012\\ Birthrate& 14.0& 13.8& 13.8& 13.8& 13.7\\ \hline\end{array}$$
a. Describe a random variable X that is associated with these data.
b. Find the probability distribution for the random variable X.
c. Compute the mean, variance, and standard deviation of X.

“Chief Grill” is a local restaurant, its annual data shows that the average sale of chicken steaks is 1200 serving per month with a standard deviation of 102. If the data is normally distributed; calculate the probability of sale of chicken steaks in the next month will be:
1. less than 1000 servings
2. more than 1400 servings
3. between 1100 to 1300 serving

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.
a. If one person on the hiring committee is chosen at random to draw the names out of a hat, what is the probability that the person drawing the names is a woman.
b. How many ways can the group who are to be hired be formed if they are no restrictions on composition?
c. How many ways can 3 database administrators be chosen?

In a survey of the number of trips abroad during one year was conduced among 1090 families. The survey reveals the following data:
$$\overline{)\begin{array}{cccccccc}\text{Number of trips}& 0& 1& 2& 3& 4& 5& 6\\ Frequency& 180& 110& 140& 150& 200& 160& 150\end{array}}$$
Which of the probabilities bellow (rounded to 2 decimal places) best represent the probability that a family makes 3 trips or less during one
a. 0.47
b. 0.40
c. 0.61
d. 0.53
e. 0.39

A survey of 70 college students showed the following data: 42 had a car; 50 had a TV; 30 had a bicycle; 17 had a car and a bicycle; 35 had a car and a TV; 25 had a TV and a bicycle; 15 had all three. How many students had none of the three items?

An insurance policy sells for $700. Based on past data, an average of 1 in 50 policyholders will file a $5,500 claim, an average of 1 in 100 policyholders will file a $10,000 claim, and 1 in 200 policyholders will file a $25,000 claim. What is the expected value of each policy the insurance company sells?

The coefficient of range of a dataset is 0.6 and the range is 60. Then the largest observation in the dataset is ?.
a. 70
b. 90
c. 20
d. 80

For 60 randomly selected college students, exam score frequency distribution was obtained. Find the Coefficient of variation for the data.
$$\begin{array}{|cc|}\hline ClassLimit& Freq\\ 5-10& 6\\ 10-15& 12\\ 15-20& 18\\ 20-25& 15\\ 25-30& 9\\ \hline\end{array}$$

Consider each distribution. Determine if it is a valid probability distribution or not, and explain your answer.
$$\begin{array}{|cccc|}\hline x& 0& 1& 2\\ P(x)& 0.25& 0.60& 0.15\\ \hline\end{array}$$

A selection process to be set in a position in GM company. Candidates are requested to complete an aptitude test. The results from the test are assumed to follow a normal distribution with standard deviation, equal to 1.3. A simple random sample of 16 results from the test has a sample mean of 4.2.
You are given a confidence interval computed by a researcher for the preceding data, going from 3.83 to 4.57. Which confidence level was used to compute this interval?
1) 82.3%
2) 78.14%
3) 74.58%
4) 67.78%

You can assess normality of data using ?
A. Pearsons

Use the following table to answer the following questions. After analyzing sales data, the owner of a mobile phone store produced the following joint probability distribution of the number of Xenia phones (X) and Yella phones (Y) sold daily.
$$\begin{array}{|cc|}\hline & \text{Xenia Phone Daily Sales}\\ \text{Yella Phones Daily Sales}& 1& 2\\ 1& 0.4& 0.1\\ 2& 0.3& 0.2\\ \hline\end{array}$$
Which phone is more likely to have two sales in a day?
1) the brands are equally likely to have two sales in a day
2) Xenia
3) you cannot determine this from the provided data
4) Yella

A car manufacturer keeps a data base of all the cars that are available for sale at all the dealerships for model A the database reports that 36% have leather 41% have a sunroof and 52% have neither determin the probability of model A car at a dealership having both leather and a sunroof

Have American males (AMs) gotten heavier over the last 20 years? A random sample 77 AMs in 2019 had a mean weight of ${\displaystyle x=189.030}$ pounds. A random sample 93 AMs in 1999 had a mean weight of ${\displaystyle y=184.795}$ pounds. It is recognized that the true standard deviation of 2019 AMs weights is
${\displaystyle {\sigma }_x=14.04}$ pounds while it is recognized that the true standard deviation of 1999 AMs weights is
${\displaystyle {\sigma }_y=10.03}$ pounds. The true (unknown) mean of 2019 AMs weights is
${\displaystyle {\mu }_x}$ pounds, while the true (unknown) mean of 1999 AMs weights is
${\displaystyle {\mu }_y}$ pounds. Weights are known to be a normally distributed. In summary:
$$\begin{array}{|cccc|}\hline Type& SampleSize& SampleMean& StandardDeviation\\ 2019Data(X)& 77& 189.030& 14.04\\ 1999Data(Y)& 93& 184.795& 10.03\\ \hline\end{array}$$
i) If we used this data to test ${\displaystyle H_0:{\mu }_x-{\mu }_y=0}$ against the alternative
${\displaystyle H_a:{\mu }_x-{\mu }_y>0}$ then what would the p value have been?
j)If we used this data to test ${\displaystyle H_0:{\mu }_x-{\mu }_y=0}$ against the alternative
${\displaystyle H_a:{\mu }_x-{\mu }_y\ne 0}$ then what would the p value have been?

Find the standard deviation for the following grouped data. Show your work.(Use 68 for the mean!)
$$\begin{array}{|cc|}\hline \text{Data Interval}& Frequency\\ 42\le x<54& 2\\ 54\le x<66& 18\\ 66\le x\le 78& 56\\ \hline\end{array}$$