Final answer:
To find the probabilities for x=pulse rates of a group of people with a mean of 76 and a standard deviation of 4, we convert the x-values to z-scores using the formula z = (x - mean) / standard deviation. For (a) p(x ≤ 73), the probability is approximately 0.2266. For (b) p(x ≥ 81), the probability is approximately 0.1056. And for (c) p(68 ≤ x ≤ 86), the probability is approximately 0.9833.
Step-by-step explanation:
To find the probabilities for x=pulse rates of a group of people, we can utilize the standard normal distribution. Given that the mean is 76 and the standard deviation is 4, we can convert the x-values to z-scores using the formula z = (x - mean) / standard deviation.
(a) To find p(x ≤ 73), we first find the corresponding z-score: z = (73 - 76) / 4 = -0.75. Using a standard normal table or a calculator, we can find that the probability is approximately 0.2266.
(b) To find p(x ≥ 81), we find the corresponding z-score: z = (81 - 76) / 4 = 1.25. Again, using a standard normal table or a calculator, we find that the probability is approximately 0.1056.
(c) To find p(68 ≤ x ≤ 86), we first find the corresponding z-scores: z1 = (68 - 76) / 4 = -2 and z2 = (86 - 76) / 4 = 2.5. By subtracting the cumulative probability of z1 from the cumulative probability of z2, we get the probability is approximately 0.9833.