Answer :
Answer:
e) [56, 76]
Step-by-step explanation:
The Empirical rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean. Those are called the middle 68%.
95% of the measures are within 2 standard deviations of the mean. Those are called the middle 95%.
99.7% of the measures are within 3 standard deviation of the mean. Those are called the middle 99.7%.
In this problem, we have that:
Mean 66, standard deviation 5
So the middle 95% is:
From 66 - 2*5 = 56 to 66 + 2*5 = 76
So the correct answer is:
e) [56, 76]
Answer:
Step-by-step explanation:
The Empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below
68% of data falls within the first standard deviation from the mean.
95% fall within two standard deviations.
99.7% fall within three standard deviations.
From the information given, the mean is 66 inches and the standard deviation is 5 inches.
the interval that contains the middle 95% would fall within two standard deviations.
2 standard deviations = 2 × 5 = 10 inches
66 - 10 = 56
66 + 10 =76
Therefore, interval that contains the middle 95% is between 56 and 76 inches