Our pulse rate is extremely important, because it is difficult to function without it! Physicians use pulse rates to assess the health of patients. A pulse rate that is abnormally high or low suggests that there might be some medical issue; for example, a pulse rate that is too high might indicate that the patient has an infection or is dehydrated.

Consider pulse rate measurements (in beats per minute) obtained from a sample of 40 females, with the results listed in Table 1 as follows:

74 68 92 62 72 68 82 64 68 68 82 76 68 72 96 72 68 72 64 82

64 82 74 74 74 80 104 86 62 76 72 72 90 80 62 66 86 86 126 64

(i) Construct a frequency distribution & relative frequency distribution for the above data with 7 classes.

(ii) Construct a Histogram with appropriate scale for the data.

(iii) Calculate the mean pulse rate of the data and also standard deviation of the data.

(iv) Past results from the National Health Survey suggest that the pulse rates (beats per minute) have a mean of 77.0 and a standard deviation of 12. Use the range rule of thumb to find the minimum and maximum "usual" pulse rates.(These results could be used by a physician who can identify "unusual" pulse rates that might be the result of some disorder). Then determine whether a pulse rate of 112 would be considered "unusual".

(v) For the sample of pulse rates of women, we have n=40 x=77 and the sample is a simple random sample. Assume that sigma is known to be 12. Using a 0.95 confidence level, find the confidence interval for m.