A lot of research is conducted on the sleeping habits of U. S. adults. One study reported that X, the amount of sleep per night of U. S. adults follows a normal distribution with mean μ=7.5 hours and standard deviation σ=1.2 hours.

Using the Standard Deviation Rule, what is the probability that a randomly chosen U. S. adult sleeps more than 8.7 hours per night?

16% probability that a randomly chosen U.S. adult sleeps more than 8.7 hours per night

Step-by-step explanation:

The Empirical Rule(Standard Deviation) states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 7.5

Standard deviation = 1.2

Using the Standard Deviation Rule, what is the probability that a randomly chosen U.S. adult sleeps more than 8.7 hours per night?

8.7 = 7.5 + 1.2

So 8.7 is one standard deviation above the mean.

By the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean. The other 100-68 = 32% are more than one standard deviation from the mean. Since the normal probability distribution is symmetric, 16% are more than one standard deviation below the mean and 16% are more than one standard deviation above the mean(above 8.7 hours)

So, 16% probability that a randomly chosen U.S. adult sleeps more than 8.7 hours per night

answer: 590

step-by-step explanation:

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.