Question

x is a normally distributed random variable with mean 40 and standard deviation 18. what is the probability that x is between 4 and 76? use the 0.68-0.95-0.997 rule and write your answer as a decimal. round to the nearest thousandth if necessary.

Answer 1

To find the probability that x is between 4 and 76, we can use the Empirical Rule. According to the Empirical Rule, the probability is approximately 0.682.

Step-by-step explanation:

To find the probability that x is between 4 and 76, we can use the Empirical Rule which states that about 68 percent of the x values lie within one standard deviation of the mean. Given that the mean is 40 and the standard deviation is 18, we can calculate the deviation from the mean for each value.

1. For x = 4, the deviation is (4 - 40) / 18 = -36 / 18 = -2
2. For x = 76, the deviation is (76 - 40) / 18 = 36 / 18 = 2

So the probability that x is between 4 and 76 is equivalent to the probability that x is between -2 and 2 standard deviations from the mean. According to the Empirical Rule, this probability is approximately 0.682.