Question

Ice cream and coins. This problem tests your understanding of the multiplication rule. Round these answers to 5 decimal places.
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 65 ounces and a standard deviation of 11 ounces.

Use the Empirical Rule, also known as the 68-95-99.7 Rule. Do not use Tables or Technology to avoid rounding errors.

Suggestion: sketch the distribution in order to answer these questions.

The following data give the average price received by fishermen for several species of fish in 2000 and 2010. The price is in cents per pound.

Fish	Year 2000 Price (x)	Year 2010 Price (y)
COD	13.1	56.0
FLOUNDER	15.3	166.7
HADDOCK	25.8	105.5
MENHADEN	1.8	41.3
PERCH	4.9	104.2
CHINOOK	55.4	236.8
COHO	39.3	135.6
ALBACORE	26.7	84.6
SOFT SHELLED CLAMS	47.5	222.6
LOBSTERS AMERICAN	94.7	374.7
SEA SCALLOPS	135.6	432.6
SHRIMP	47.6	225.4

1. Create a regression equation for the data.
   
   ˆy=y^= Round to 2 decimal places.
   
2. What is the correlation coefficient between the 2000 and 2010 prices.
   
   Round to 2 decimal places.
   
3. If a type of fish was 41.3 cents per pound in 2000, how much would you expect to pay for it in 2010?
   
   ¢/lbs Round to 1 decimal places.

Answer 1

a)

We will be applying the Linear regression model here, it can be done by using the function LINEST(y_value, x_value, TRUE, TRUE) where y_values contain values of the Year 2010 prices here and x_values have the Year 2000 prices values.

Select 5 rows and 2 columns and then write the formula in the first cell and after that, press Shift + Ctrl + Enter.    

The equation comes out to be -

y = 55.77 + 2.99*x  

b)

The correlation coefficient comes out to be 0.9512 here.

c)

When x = 41.3

y = 55.77 + 2.99*41.3

y = 55.77 + 123.487

y = 179.257

The year price 2010 is 179.257 cents at the year price 2010 of 41.3 cents.