The length of time needed to complete a certain test is normally distributed with mean 57 minutes and standard deviation 8 minutes. a. What is the relative frequency of people who take between 49 and 65 minutes to complete the test? Sketch the distribution and shade in the area in question. b. Find the interval that contains the middle 95% of completion times for all people taking the test.

(a) The relative frequency of people who take between 49 and 65 minutes to complete the test is 0.6826.

(b) The  middle 95% of completion times for all people taking the test is in the interval (41, 73).

Step-by-step explanation:

Let X = length of time required complete a certain test.

It is provided that X follows a Normal distribution with mean, μ = 57 minutes and standard deviation, σ = 8 minutes.

(a)

Compute the probability of people who take between 49 and 65 minutes to complete the test as follows:

*Use the z-table for the probability.

Thus, the relative frequency of people who take between 49 and 65 minutes to complete the test is 0.6826.

The graph is provided below.

(b)

According to the Empirical rule, for a normal distribution:

Then, P (μ - 2σ < X < μ + 2σ) = 0.95

Compute the limits as follows:

Thus, the  middle 95% of completion times for all people taking the test is in the interval (41, 73).

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

answer: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

step-by-step explanation: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.