1. The eruption height and the time interval after eruption of a geyser were measured and are shown below. Answer part a-c.

Height (x) 120 110 125 140 140 120 150 125

Interval after (y) 94 65 40 55 92 94 87 101

a. Find the value of the linear correlation coefficient r.

r=….. (Round to three decimal places as needed)

b. Find the critical values of r from the table showing the critical values for the Pearson correlation coefficient using 0.05.

The critical values are ±….. (Round to three decimal places as needed)

c. Is there sufficient evidence to conclude that there is a linear correlation between the two variables?

A. Yes, because the absolute value of the correlation coefficient is less than the critical value.

B. Yes, because the absolute value of the correlation coefficient is greater than the critical value

C. No, because the absolute value of the correlation coefficient is less than the critical value

D. No, because the absolute value of the correlation coefficient is greater than the critical value.

(Show work)

2. Assume that thermometer readings are normally distributer with a mean of 0⁰C and a standard deviation of 1.00⁰C. A thermometer is randomly selected and tested. For the case below, draw a sketch and find probability of reading. (The given values are in Celsius degrees.)

Between -1.12 and 1.57

a. Draw a sketch.

b. The probability of getting a reading between -1.12⁰C and 1.57⁰C is ……. (Round to four decimal places as needed)