Max's cell phone plan charges a monthly

6.5% of people in the U.S. Have A- blood type. You randomly select 6 Americans and ask them if their blood type is A-. a) Find t

Keith_Richards [23]

Answer:

a) 7.54189*10^-8

b) 0.99999999

c) E ( X ) = 0.39 , s ( X ) = 0.604

Step-by-step explanation:

Solution:-

- We will assume the proportion of people with A- blood group is independent and remains constant for a fairly small sample of n = 6 Americans selected at random.

- We will denote a random variable X = The number of americans out of 6 that have blood group type A-.

- The random variable is assumed to follow binomial distribution.

- The probability of success is the proportion of people in U.S that have blood group type A-, p = 0.065:

X ~ Bin ( 6 , 0.065 )

Where, r represents the number of americans out of selected 6 have blood group A-. The pmf of a binomial variate is given as:

P ( X = r ) = nCr * ( p ) ^r * ( 1 - p ) ^ ( n - r )

a) Find the probability that all 6 are type A-

- We will pmf given above and set r = 6. And evaluate the resulting probability:

P ( X = 6 ) = 6C6 * ( p )^6 * ( 1 - p ) ^ ( 0 )

= p^6

= ( 0.065 )^6

= 7.54189*10^-8

b) Find the probability that at most 4 of them are type A-

- We will pmf given above and evaluate the following expression:

P ( X ≤ 4 ) = 1 - P ( X = 5 ) - P ( X = 6 )

P ( X ≤ 4 ) = 1 - 6C5 * ( p )^5 * ( 1 - p ) ^ ( 1 ) - p^6

= 1 - 6*(0.065)^5 ( 0.935 ) - 0.065^6

= 1 - 6.50923*10^-8 - 7.54189*10^-8

= 0.99999999

c) Find the mean and standard deviation.

- The mean E ( X ) of the defined random variable distributed binomially is given by:

E ( X ) = n*p = 6*0.065 = 0.39 people

- The mean s( X ) of the defined random variable distributed binomially is given by:

s ( X ) = √n*p*q = √(6*0.065*0.935) = 0.604

5 0

2 years ago

Suppose that normal human body temperatures are normally distributed with a mean of 37°C and a standard deviation of 0.2°C. The

saveliy_v [14]

Answer:

Step-by-step explanation:

The answer is not 15.87%

4 0

2 years ago

Read 2 more answers

Write an equation perpendicular to x-4y=20 that passes through the point 2,-5

marshall27 [118]

Answer:

4x +y = 3

Step-by-step explanation:

Perpendicular lines have slopes that are the negative reciprocals of one another. When the equation of the line is written in standard form like this, the equation of the perpendicular line can be written by swapping the x- and y-coefficients and negating one of them. Doing this much would give you ...

4x +y = (constant)

Note that we have chosen to make the equation read 4x+y, not -4x-y. The reason is that "standard form" requires the leading coefficient to be positive.

Now, you just need to make sure the constant is appropriate for the point you want the line to go through. So, it needs to be ...

4(2) +(-5) = constant = 3

The line of interest has equation ...

4x + y = 3

3 0

2 years ago

A tree makes a shadow that is 14 ft long. Rachel is 6 ft tall. when she id standing near the tree, her shadow is 3.5 ft long. wh

ankoles [38]

The triangle that is formed from by connecting the shadow, the tree and the endpoints of each is a right triangle. The two triangles formed (by the tree and its shadow, and by Rachel and her shadow) are similar. In similar triangles, the corresponding sides are proportional. Thus, to give the numerical answer to this item,
length of the tree/14 ft = 6 ft / 3.5 ft
length of the tree = 24 ft

5 0

2 years ago

While visiting Yosemite National Forrest, Joe approximated the angle of elevation to the top of a hill to be 40 degrees. After w

NARA [144]

Draw a diagram to illustrate the problem as shown in the figure below.

Let h = the height of the hill.
At position A, the angle of elevation is 40°, and the horizontal distance to the foot of the hill is x.
By definition,
tan(40°) = h/x
h = x tan40 = 0.8391x (1)

At position B, Joe is (x - 450) ft from the foot of the hill. His angle of elevation is 40 + 18 = 58°.
By definition,
tan(58°) = h/(x - 450)
h = (x - 450) tan(58°) = 1.6003(x-450)
h = 1.6003x - 720.135 (2)

Equate (1) and (2).
1.6003x - 720.135 = 0.8391x
0.7612x = 720.135
x = 946.0523

From (1), obtain
h = 0.8391*946.0523 = 793.8 ft

Answer: The height of the hill is approximately 794 ft (nearest integer)

8 0

2 years ago