Question

6. Explain the meaning of the 85' percentile of this distribution 8) Do the sample data give a close approximation to the theoretical distribution? In complete sentences, compare the empirical statistics and the theoretical statistics to explain why or why not.

please help me answer the question in the first photo using the data from second photo

Answer 1

1. From the given data, the frequency distribution is

125 Class Interval LL UL 126.9 127 128.9 129 130.9 131 132.9 133 134.9 Total =

2. Histogram:

Histogram 11 125-126.9 127-128.9 129-130. 9 1 301-132.9 133-134.9

8. The shape of the histogram is bell - shaped that means it is symmetric distribution

From the frequency distribution

UL 125 Class Interval LL 126.9 127 128.9 129 130.9 132.9 133 134.9 Total = Mid values (xi) 125.95 127.95 129.95 131.95 133.95 fixi 755.7 1023.6 1429.45 923.65 535.8 4668.2 fixin2 95180.42 130969.6 185757 121875.6 71770.41 605553.1 131

--4668.2 = 129.672 Mean X = = 4668.2 = 129.672 ----[<«-ni]-3-(6058531- 36(129672* )= 6,2054 Sample variance Sample SD: S= 16.2064 = 2.49

Empirical Rule: If the whole data follows normal distribution then i) the data falls within one SD from the mean is 0.6827 ie. P(4-0<x<4+0) = 0.6827 ii) the data falls within two SD from the mean is 0.9545 ie. P(4-20<x<4+20) = 0.9545 ioi) the data falls within three SD from the mean is 0.9973 ie. P(4-30<X<4+30) = 0.9973 Practically rule : i) ats=(3-5,x+5)= (129.672 - 2.49,129.672+2.49) = (127.182,132.162) The number of values lies between the above interval is 23 Proportionality = 23162 = 0.6389 ii) x+2s =(x-25,x+2) = (129.672-2*2.49,129.672+2*2.49)=(124.692,134.652) The number of values lies between the above interval is 36 Proportionality=36/36=1 III) x+3s =(x-3s,x+3s) = (129.672-3*2.49,129.672+3*2.49)= (122.202,137.142) The number of values lies between the above interval is 36 Proportionality=36/36=1 Since the probabilties are not closed to empirical probabilites

Therefore, the distribution is not follows normal distribution