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Complete Question
Assume that females have pulse rates that are normally distributed with a mean of u = 76.0 beats per minute and a standard deviation of 12.5 beats per minute. If 1 adult female is randomly selected, find the probability that her pulse rate is between 70 beats per minute and 82 beats per minute. The probability is (Round to four decimal places as needed.)
Answer:
0.3688
Explanation:
The formula for calculating a z-score when given a random sample of numbers is is z = (x-μ)/σ/√n
where x is the raw score,
μ is the population mean, and
σ is the population standard deviation.
mean = 76.0 beats per minute and a standard deviation = 12.5 beats per minute.
n = number of random samples = 1
For 70 beats per minute
z = 70 - 76/12.5/√1
z = -0.48
Probability value from Z-Table:
P(x = 70) = 0.31561
For 82 beats per minute.
z = 82 - 76/12.5/√1
z = 0.48
Probability value from Z-Table:
P(x = 82) = 0.68439
The probability that her pulse rate is between 70 beats per minute and 82 beats per minute.
P(x = 82) - P(x = 70)
0.68439 - 0.31561
= 0.36878
≈ 0.3688