Question

1. Th in the table below e average sales (in Millions) of a company for the time period of 1995-200S are given Using the sales data in the table calculate the following (show work where possible) a. Sales in z-Score Millions Year 1. Mode?beee ne+ exic) 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 1.47 14 1.52 1.75 1.82 2.050 54 999 2.25 32977 2.55 3.20 3.50 3.85 4.10 2. Median 2.2 .37779 3. Mean .5509 4. Standard Deviation-4?ss o. 00 711292 94018 1042377 Draw a scatter plot for the data. 7-5 Find the equation of the line of best fit and interpret the slope and y intercept in the context of the problem. c. e regression equahen:s What is the correlation coefficient and interpret it in the context of the problem. Using the line of best ft from the previous question predict the average sales in d. uec lin ofiertontom t riag.greati e. 2cso ?) millions for the year 2050.

Answer 1

Almost all your working is correct, except for onr thing - the standard deviation is not 4.055. It cannot be, since the values themselves do not fall in that range - the highest value, 4.10 just crosses it.

$\textup{St. Deviation, }\sigma \approx 0.9124\textup{ (Population statistic)}$

The regression parameters are all good. but since the standard deviation has changed, the Z-scores shall change, which can now be corrected using this St. Dev. value - your formula is correct.

g. Using St. Dev. value, the Z score is

$Z=\frac{X-\mu }{\sigma }=\frac{3.75-2.5509}{0.9124}=1.3142$

$\textup{Required probability}=P(Z>1.3142)=0.0944$

h. For the central 75% range of sales, we require the Z score such that

$P(-z<Z<z)=0.75$

$\Rightarrow P(0<Z<z)=0.375$

$\Rightarrow z=1.15035$

Hence, the required range can now be constructed as

$\mu-z\sigma<\textup{Sales}_{0.75}<\mu +z\sigma$

$2.5509-1.15035\times 0.9124<\textup{Sales}_{0.75}<2.5509+1.15035\times 0.9124$

$1.5<\textup{Sales}_{0.75}<3.6$