Answer:
Between the lower-bound of 117 mg/dl and the upper bound of 137 mg/dl.
Step-by-step explanation:
Empirical Rule
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Central Limit Theorem:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
In this question:
Mean of 127, standard deviation of 10.
For the sample mean:
By the Central Limit Theorem, mean is 127, while the standard deviation is
According to the empirical rule, in 95 percent of samples the SAMPLE MEAN blood-glucose level will be between?
By the Empirical Rule, within 2 standard deviations of the mean. So
127 - 2*5 = 117 mg/dl
127 + 2*5 = 137 mg/dl.
Between the lower-bound of 117 mg/dl and the upper bound of 137 mg/dl.