Fatouma draws a card at random from a standard deck of 52 playing cards

A survey conducted by the Consumer Reports National Research Center reported, among other things, that women spend an average of

Nookie1986 [14]

Answer:

(a) The probability that a randomly selected woman shop exactly two hours online is 0.217.

(b) The probability that a randomly selected woman shop 4 or more hours online is 0.0338.

(c) The probability that a randomly selected woman shop less than 5 hours online is 0.9922.

Step-by-step explanation:

Let X = time spent per week shopping online.

It is provided that the random variable X follows a Poisson distribution.

The probability function of a Poisson distribution is:

$P (X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!} ;\ x=0,1,2,...$

The average time spent per week shopping online is, λ = 1.2.

(a)

Compute the probability that a randomly selected woman shop exactly two hours online over a one-week period as follows:

$P (X=2)=\frac{e^{1.2}(1.2)^{2}}{2!} =0.21686\approx0.217$

Thus, the probability that a randomly selected woman shop exactly two hours online is 0.217.

(b)

Compute the probability that a randomly selected woman shop 4 or more hours online over a one-week period as follows:

P (X ≥ 4) = 1 - P (X < 4)

= 1 - P (X = 0) - P (X = 1) - P (X = 2) - P (X = 3)

$=1-\frac{e^{1.2}(1.2)^{0}}{0!}-\frac{e^{1.2}(1.2)^{1}}{1!}-\frac{e^{1.2}(1.2)^{2}}{2!}-\frac{e^{1.2}(1.2)^{2}}{3!}\\=1-0.3012-0.3614-0.2169-0.0867\\=0.0338$

Thus, the probability that a randomly selected woman shop 4 or more hours online is 0.0338.

(c)

Compute the probability that a randomly selected woman shop less than 5 hours online over a one-week period as follows:

P (X < 5) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4)

$=\frac{e^{1.2}(1.2)^{0}}{0!}+\frac{e^{1.2}(1.2)^{1}}{1!}+\frac{e^{1.2}(1.2)^{2}}{2!}+\frac{e^{1.2}(1.2)^{3}}{3!}+\frac{e^{1.2}(1.2)^{4}}{4!}\\=0.3012+0.3614+0.2169+0.0867+0.0260\\=0.9922$

Thus, the probability that a randomly selected woman shop less than 5 hours online is 0.9922.

8 0

4 years ago

What is the circumference of a circle with diameter of 10.4 cm?

bekas [8.4K]

The circumference of a circle:

2丌r

In this case, the radius:

10.4÷2

=5.2cm

The circumference

=2兀(5.2)

=2(5.2)兀

=10.4兀

Therefore the answer is 10.4兀.

Hope it helps!

5 0

4 years ago

In this PARALLELOGRAM, what is the measure of Angle D?

enot [183]

Answer:

92

Step-by-step explanation:

The parallelogram is divided into two triangles. Remember, angles in a triangle add up to 180 degrees. That being said, take the sum of the numbers given in triangle ABC and subtract it from 180.

60 + 28 = 88

180 - 88 = 92 (this is the measure of angle B)

Angles D and B are congruent, which means they are the same.

Since Angle B is 92 degrees, then D is 92 degrees also.

8 0

3 years ago

Find the value of x- plz helppp mee

maw [93]

Answer:

67.5

Step-by-step explanation:

Im pretty sure this is the answer. A triangle is 180º so you do 180-45 and divide it by 2.

4 0

3 years ago

Read 2 more answers

what is the distance around a triangle that has sides measuring 2 and one eight feet , 3 one half feet, and 2 one half feet?

Ymorist [56]

Perimeter = 2 1/8 + 3 1/2 + 2 1/2 = 8 1/8

4 0

3 years ago