Question

Assume that females have pulse rates that are normally distributed with a mean of p = 72.0 beats per minute and a standard deviation of a Complete parts (a) through (c) below. 12.5 beats per minute. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 76 bens per minute The probability is (Round to four decimal places as needed.) b. It 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 76 beats per minute. The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 307 O A. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size O B. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. O C. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size. OD. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size. Click to select your answer(s). This course Elementary Statistics 13th Edition is based on Trio Elementary Statistics 13e

Answer 1

solution :- mean of female pulse rate per min (u) = 72 standard deviation of pulse rate (o)= 12.5 Let & be pulse rate per minute of a randomly selected female (as p(xc76) ? since & has normal distribution, it can be converted to standard normaly by ereplacing x with z=x-4 z - value for x=16 is → z =76-4 - 76-12 - 0.32 - 12 .5 P( xc76)=P(Z <0.32) feom z table, P(Z <0.32) = 0.6255 0.6255 P(x<76) = (6) no. of adult females in sample (n) =25 . We have to calculate p(x<76) ?