Use the following data set: 7,17,30,18,24,16,3,18,7 to answer questions The data

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.

Explain about of the measure of central tendency that is most appropriate for these data.

For healthy adults, the mean pH level is ${\displaystyle \mu =7.4}$, a new drug for arthritis has been developed. However, it is throught that this drug may change blood pH. A random sample of 33 patients with arthritis took the drug for three months. Blood tests showed that the sample mean from these 33 patients was a pH of 8.0 and it is known that ${\displaystyle \sigma =2.3}$. (Note, there is no unit for this type of data). Use ${\displaystyle \alpha =0.05}$ level of significance to test the claim that the drug has increased the mean pH level of the blood.
If we use the classical approach, what would the criterion (step 3) be?
1) -1.645 or less
2) -2.33 or less
3) 1.645 or more
4) 2.33 or more

The probabilities of a machine manufacturing 0, 1, 2, 3, 4 or 5 defective parts in one day are 0.75, p, 0.04, 0.025, 0.01 and 0.005 respectively. Construct a probability distribution for the data, by finding the missing probability. Also find the mean and variance.

You fit a CAPM that regresses the excess return of Coca-cola on the excess market return using 20 years of monthly data. You estimate ${\displaystyle \alpha =0,72,\beta =1,37,S^2=20,38,{\sigma }_X^2=19,82\text{and}{\mu }_x=0,71}$.
What are the standar errors of ${\displaystyle \alpha \text{and}\beta }$?

An advertising campaign for a new product is tergeted to make 20% of the adult population in a metropolitan area aware of the product. After the campaign, a random sample of 400 adults in the metropolitan area is obtained.
i. Find the approximate probability that 57 or fewer adults in the sample are aware of the product.
ii. Should the approximation in part i. be accurate?

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