Question

*THERE IS A BACK PAGE (10pts Total) Base the following questions ketch of the distribution of heights for students in Math 147 Base the following questions on the histogram shown below, which give 78 inches 54 inches Figure 1: Class Heights Note that it is approximately normal, and the sketch is drawn so that the curve touches the -axis at 54" and r 78". Give all answers corresponding to heights to the nearest inch 1. (If you don't know the answer, guess so you can use something in question 2.) (A) Based on how the histogram is drawn, what is the standard deviation? Give your answer to the nearest inch. (2pts) (b) Based on how the histogram is drawn, what is the mean of the data? (2pts)

Answer 1

Solution-A

as it touches the curve

99.7% of the values lies within 3 sd of the mean

mean-3*sd=54---(1)

mean+3sd=78---(2)

2*mean=54+78

mean=66

substitute in (1) we get

66-3*sd=54

sd=66-54/3

sd=12/3=4

standard deviation=4 inches

Solution-B;

mean of the data -centre line in normal curve=66