Suppose the following tables present the number of specimens that tested positive for Type A and Type B influenza in a country during a flu season. Type A 38 100 186 199 253 380 595 966 1611 2638 3845 4931 5183 5367 5890 Type B 59 95 116 143 156 225 271 366 495 696 851 1060 1140 1101 1202 Send data to Excel (a) Find the mean and median number of Type A cases. Round the answers to at least one decimal place. (b) Find the mean and median number of Type B cases. Round the answers to at least one decimal place. (c) A public health official says that there are more than twice as many cases of Type A influenza than Type B. Do these data support this claim

(a) Mean and Median of type A

(b) Mean and Median of type B

(c) The claim by the public health worker is true.

Step-by-step explanation:

Given

Solving (a): The mean and median of A.

Mean is calculated using:

The median is calculated using:

The 8th item is: 966

So:

Solving (b): The mean and median of B.

Mean is calculated using:

The median is calculated using:

The 8th item is: 366

So:

(c) The claim by the public health worker is true.

To do this, we simply compare the mean value of both types.

For Type A

For Type B

The claim is:

Since the inequality is true, then the claim is true

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)

in counting the number of heads in 4 coin flips, the probability that we get exactly one head is the probability that we get anyone of the following 4 outcomes: httt, thtt, ttht, or ttth. each has probability 1/16, so the probability to get exactly one head in 4 flips is 1/16 + 1/16 + 1/16 + 1/16 = 4/16 = 1/4.