Question

We think the number of stomach contractions in healthy patients should follow a normal distribution. The sample mean number of stomach contractions per minute in healthy patients is 260.12 contractions with a sample standard deviation of 247.94 contractions. Determine the proportion of patients with fewer than 500 stomach contractions per minute using each of the following two methods:  

1. Calculate the actual proportion of patients with less than 500 stomach contractions per minute by counting the sample cases (Hint: use the countif and count functions in excel)

Answer 1

Sol:

P(xbar<500)

z=x-mean/sd

P(Z<500-260.12/247.94)

P(Z< 239.88/247.94 )

P(Z< 0.9675)

from normal distribution table

=0.8334

0.8334

the proportion of patients with fewer than 500 stomach contractions per minute =0.8334

For second part

excel data needed

1. Calculate the actual proportion of patients with less than 500 stomach contractions per minute by counting the sample cases (Hint: use the countif and count functions in excel)
2. provide excel sheet