The temperature recorded by a certain thermometer when placed in boiling water (true temperature 100 degree C) is normally distributed with mean p=99.8 degree C and standard deviation sigma =1-1 degree C. a) What is the probability that the thermometer reading is greater than 100 degree C? b) What is the probability that the thermometer reading is within +- 0.05 degree C of the true temperature? c) What is the probability that a random sample of 30 thermometers has a mean thermometer reading is less than 100 degree C? (inclusive)

a) The probability that the thermometer reading is greater than 100 degree C is approximately 0.1587.

b) The probability that the thermometer reading is within +- 0.05 degree C of the true temperature is approximately 0.3830.

c) The probability that a random sample of 30 thermometers has a mean thermometer reading less than 100 degree C is approximately 0.0001.

a) Using the Z-score formula, we get Z = (100 - 99.8)/1.1 = 0.182. Looking up the standard normal distribution table, we find the probability of a Z-score being greater than 0.182 is 0.1587.

b) To find the probability that the thermometer reading is within +- 0.05 degree C of the true temperature, we need to find the area under the normal distribution curve between 99.95 and 100.05.

Using the Z-score formula for the lower and upper limits, we get Z1 = (99.95 - 99.8)/1.1 = 0.136 and Z2 = (100.05 - 99.8)/1.1 = 0.364. Looking up the standard normal distribution table for the area between Z1 and Z2, we find the probability is 0.3830.

c) The sample mean follows a normal distribution with mean 99.8 and standard deviation 1.1/sqrt(30) = 0.201. Using the Z-score formula, we get Z = (100 - 99.8)/(0.201) = 0.995. Looking up the standard normal distribution table for the area to the left of Z, we find the probability is approximately 0.0001.

For more questions like Probability click the link below:

https://brainly.com/question/30034780

#SPJ11

- A unicycle tire has a radius of 13 inches. About how far will the unicycle travel in 20 rotations?
F.1633 inches
G.10,613 inches
H.82 inches
J.520 inches

find the value of -
[tex]( {x}^{2} - x)[/tex]
where, x = 5
​

Slope of 4,-9 and 8,-3

Find the equation of the line that passes through both points (6,-5) (0,3)

if the slop of the straight line passing through the two points A (4, k) , B (3, 2) is 5, find the value of K

Angel repairs used furniture. He expects to use 48 oz of wood filler this month. There are 16 oz in 1 lb. How many pounds of wood filler does Angel expect to use this month?

On a loan of $4,500 for 2 1/2 years at 4% per year, how much do you wind up paying to pay off the loan?

PLS SHOW HOW YOU SOLVED THE PROBLEM
15. The perimeter of an isosceles triangle is 34 inches. When you add the base of the
triangle to one of the equal sides the sum is 18. What is the length of the base of the
triangle?
a)
2 inches
go to card 3
b) 14 inches
go to card 6
c) 9 inches
go to card 9
d) 16 inches
go to card 11
e) 4 inches
go to card 13

A CIRCLE HAS A CIRCUMFENCE 43.96 YD FIND THE RADUIS OF THE CIRCLE

Pedro tiene 335 en monedas de 5 y de 10, si en total tiene 52 monedas ¿cuantas monedas tiene de cada una?

ayuda por favor​

Find the point-slope equation for the line that passes through the points (-6, 24) and (5, -31). Use the first point in your equation. y - [?] = [ ](x-[ ])​

Find the slope of a graph
I'll GIVE BRAINLESS

if sin theta = cos theta,theta is an acute angle then tan theta=?
please answer within one hour
I will mark u brainliest​

Polar bears eat 8.4 pounds of fish a day. Penguins eat about 0.80 of that amount. How many pounds if fish do penguins eat?

Can you answer this for 20 points? With which countries was France at war in 1792 and 1793?

A rectangle has a length of 2y inches and a width of y - 4 inches. If the perimeter of the rectangle is 22 inches, what is y? What is the length? What is the width?

George wants to buy a new television that is on sale for 1/4 off the regular price of $599.96. The sales tax is 7%. What is the final price of the television including tax? ​

The y-intercept of the the inverse of the function f(x) = 1/4 x-9/4 is

Need help ASAP 25 points

I NEED HELP NOW ITS DUE TODAY AND I HAVE MORE AHHHHHHHHH
Lin needs to save up $20 for a new game. How much money does she have if she has saved 25% of her goal?

Can someone please help me ASAP

pls help me with this I have to go to bed soon( I need the volume of the sphere)

Rearrange p=r+3 to make r the subject

The entire digits of pie times the square root of 1

A sailboat with a sick passenger abroad is following a parabolic path given by the equation = − 2 +2 + 8.
The boat’s captain sent out a distress signal. A speedboat is trying to catch the sailboat to provide medical aid and is on a path given by the linear equation y=- x+8. Besides the y-intercept (starting location) where do the paths of the two boats cross (for each graph you must plot at least 3 points each and give answer in coordinate pair notation)?

the length and breadth of a hall are 20m and 15m respectively. find the area of 4 Walls of the hall if the height of the hall is 10 m​

A savings account earns 7% interest each year, compounded quarterly (4 times a year). If a person invests $300 and makes no further deposits or withdrawals, what is the balance in the account after 5 years​

3x-4y=-14 6x+3y=27 don’t understand how to solve

Find the square root. 1/16​

1/4 y + 9=1/2 A -34 b 2 c 9 d 38