STAT10 Lab 5

Week 6 Stat 10 Page 3 of 8 2. Recall: 68-95-99.7 Rule For a data set which is mound-shaped or approximately mound-shaped (i.e., normal or approximately normal), the following statements will hold: ●  68% of the observations will lie within    . ●  95% of the observations will lie within 2    . ●  99.7% of the observations will lie within 3    . Consider a r.v., Z , with a standard normal distribution. We can confirm each of the statements in the 68-95-99.7 Rule using the Z table on Page 410-411 of the textbook. Note: Since ( ) ~ 0,1 Z N , we have 0  = and 1  = . 1) Statement 1:  68% of the observations will lie within    a) What is the numerical value for the lower bound (LB) of the interval?_____ -1 ________ b) What is the numerical value for the upper bound (UB) of the interval? ______ 1 _______ c) We are interested in ( ) P LB Z UB   . Complete the sketch for this probability. d) Find ( ) P LB Z UB   . 0.8413 – 0.1587 0.6826 2) Statement 2:  95% of the observations will lie within 2   

Week 6 Stat 10 Page 6 of 8 Z = -0.666 P = 0.2546 2) What proportion of adults will have pulse rates between 60 and 100? Z = (60 -78)/12 Z = -1.5 P = 0.0668 Z = (100 -78)/12 Z = 1.833 P = 0.9664 1.833 – 1.5 = 0.8996 3) What is the 95 th percentile for the pulse rates of adults? Z = 1.645 1.645 = (x – 78)/12 (1.645*12) + 78 = x 97.74