The manager of a vacation resort believes that the ages of adult visitors to the resort can be modeled by a normal distribution. The manager surveyed a random sample of 765 visitors and recorded their age. A summary of the responses is shown in the frequency table, where x represents the age of the visitor.

(a) Construct a histogram of the distribution of ages.
(b) Write a few sentences to describe the distribution of ages of the adult visitors to the resort.
(c) Does the histogram provide convincing evidence that the surveyed ages come from a normal distribution? Explain your answer.

Age (years) Frequency
20≤x<30 160
30≤x<40 130
40≤x<50 100
50≤x<60 115
60≤x<70 125
70≤x<80 135

Step-by-step explanation:

(a) A histogram is like a bar graph, but with ranges instead of values.

(b) The distribution is approximately uniform, with slightly more people at the younger and older ends than in the middle.

(c) The ages do not appear to come from a normal distribution.  Normal distributions are bell-shaped, tall in the middle and short on the sides.

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4