The hourly median power (in decibels) of received radio signals transmitted between two cities
follows a lognormal distribution with parameter values u = 3.5 and o2 = 1.22.

(5 points) What is the 90th percentile of this distribution?

(5 points) What is the probability that received power for one of these radio signals is
less than 150 decibels?

(5 point) Consider a random sample of 10 radio signals. What is the probability that for
6 of these signals, the received power is less than 150 decibels?

Using the lognormal and the binomial distributions, it is found that:

In a lognormal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{\ln{X} - \mu}{\sigma}[/tex]

In this problem:

Question 1:

The 90th percentile is X when Z has a p-value of 0.9, hence X when Z = 1.28.

[tex]Z = \frac{\ln{X} - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{\ln{X} - 3.5}{\sqrt{1.22}}[/tex]

[tex]\ln{X} - 3.5 = 1.28\sqrt{1.22}[/tex]

[tex]\ln{X} = 1.28\sqrt{1.22} + 3.5[/tex]

[tex]e^{\ln{X}} = e^{1.28\sqrt{1.22} + 3.5}[/tex]

[tex]X = 136[/tex]

The 90th percentile of this distribution is of 136 dB.

Question 2:

The probability is the p-value of Z when X = 150, hence:

[tex]Z = \frac{\ln{X} - \mu}{\sigma}[/tex]

[tex]Z = \frac{\ln{150} - 3.5}{\sqrt{1.22}}[/tex]

[tex]Z = 1.37[/tex]

[tex]Z = 1.37[/tex] has a p-value of 0.9147.

There is a 0.9147 = 91.47% probability that received power for one of these radio signals is  less than 150 decibels.

Question 3:

10 signals, hence, the binomial distribution is used.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, we have that [tex]p = 0.9147, n = 10[/tex], and we want to find P(X = 6), then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 6) = C_{10,6}.(0.9147)^{6}.(0.0853)^{4} = 0.0065[/tex]

There is a 0.0065 = 0.65% probability that for  6 of these signals, the received power is less than 150 decibels.

You can learn more about the binomial distribution at https://brainly.com/question/24863377

Which situation involves permutations? A. choosing 5 people out of 15 to participate in a survey B. choosing 3 flavors of ice cream out of 15 for an ice-cream sundae C. choosing a dozen flowers out of 30 to create a bouquet D. choosing first second-, and third-place winners in a cooking contest​

Please help!!!

A. (-4,2)

B. (-4,-2)

C. (2,-4)

D. (2,4)

the length of a rectangle is 4 less than 3 times its width.if its width is 5 cm what will be its perimeter​

Put the numbers from least to greatest
3.55
3.544
3.554

a college student is saving money to buy a laptop. the student has $85 saved and saves $35 each week. The function a(t)=35t + 85 represents the amount of money the college student has saved for the laptop after t weeks. The student receives $50 as a birthday gift .
If the function f(t) = a(t) +50 represents the total amount the student has saved , which best describes the transformation from a(t) to f(t)?

Simplify 7x + [x - (5 + x)].
O 7x - 5
O8X-5
9x - 5

evaluate (2/3)6 power
evaluate 2/3 evaluate 2/3 6th power ​

Consider the graph of the of the quadratic function g(x). See below

thanks i'll mark brainliest ​

Find the difference of 651

8m – 5 for m = 9 answer please

help please ill give the person who answeres honstly a biranly and 25 points ofc ofc

what is the ratio of 5:2

2x5 what would 2x5=?

Fireman Bob leans a 40 foot ladder against a building at an angle of elevation of 70'. How far is the base of the ladder from the building (round your
answer to the nearest thousandth)?
Distance from base of the building

help me out guys !!!?​

Which relation is not a function?​

Victor drives a distance of 21.45 miles everyday from home to his office. He moves into a new apartment that is just 3.65 miles away from his office. Determine the distance by which Victor has lessened his drive to the office.

A farmer had 21 goats all but 9 died how many survive ?

The price of a video game is $32.99 before tax. Andre bought the video game for 20% off. He then paid 8% sales tax on the discounted price. Part A: How much did Andre pay in sales tax? Show all work and steps in your solution. (5 points) Part B: What is the total amount that Andre paid for the video game? Show all work and steps in your solution. (5 points)

Please take a look at the picture

Find the following limit without using a graphing calculator or making a table.

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 14 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area. (Round your answer to two decimal places.)

brainliest
chose a point below that lies on the function y -10=-3(x-2)
(2,10)
(-3,2)
(-2,-3)
(10,2)

A store sells six cupcakes for $7. How much do 18 cupcakes cost?

If h(x)=5x+7, then h(x) has a zero at which of the following values?
(1) -5
(2) 7
(3) -1.4

perform the operation and simplify

help plz we this work

the current population of earth is estimated to be about 7,440,000,000. express number in scientific notation

Simplify.

510√




2√

2√2

10√2

5√