The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.60° F. If 25 adults are randomly selected, find the probability that their mean body temperature is less than 99° F?

Answers

Answer 1

Answer:

Answer: 0.9996

Step-by-step explanation:

Given : The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.60° F.

Sample size : n=25

Let x be the random variable that represents the body temperatures of adults.

z-score : $z=(x-\mu)/((\sigma)/(√(n)))$

For x= 99° F

$z=(99-98.6)/((0.60)/(√(25)))\approx3.33$

Now, the probability that their mean body temperature is less than 99° F will be :-

$P(X<99)=P(z<3.33)=0.9995658\approx0.9996$

Hence, the probability that their mean body temperature is less than 99° F = 0.9996

Answer 2

Answer:

Final answer:

To find the probability that the mean body temperature of 25 randomly selected adults is less than 99°F, we can use the Central Limit Theorem and calculate the Z-score. The mean body temperature of adults is 98.6°F with a standard deviation of 0.60°F. The sample size is 25.

Explanation:

To find the probability that the mean body temperature of 25 randomly selected adults is less than 99°F, we can use the Central Limit Theorem. According to the Central Limit Theorem, the sampling distribution of the sample mean follows a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, the mean body temperature of adults is 98.6°F with a standard deviation of 0.60°F. The sample size is 25. So, the mean of the sampling distribution would still be 98.6°F, but the standard deviation would be 0.60°F divided by the square root of 25, which is 0.12°F.

Now, we can use the Z-score formula to find the probability that the mean body temperature is less than 99°F. The Z-score is calculated by subtracting the population mean from the desired value (99) and dividing it by the standard deviation of the sampling distribution (0.12). We can then use a Z-table or calculator to find the probability associated with the Z-score.

Learn more about Probability here:

brainly.com/question/32117953

#SPJ3

Related Questions

What is the product of 2x + y and 5x – y + 3?
What is a real situation that would be represented by a+3
A scientist is working with 13 meters of gold wire. How long is the wire in millimeters?
A car travels 36 miles in 1 hour and 30 minutes, what is its average speed
Please help if you know how to do Similarity in Geometry!!

I am confused on numbers 25 and 29, the instructions are at the top.

Answers

#25 is fairly simple. Plug in -4 and 3 into the equation, and the extraneous root will be the one that does not work.
$√(12-(-4)) = √(16) = \frac{+}{}4$
Extraneous root in this case is positive four since +4≠-4
$√(12-3) = √(9) = \frac{+}{}3$
In this case it's negative 3, since -3≠3

#29 can be turned into a quadratic equation.
$x= √(2x+3)$
Square both sides to get
$x^(2)=2x+3$
Then bring the 2x+3 to the other side, setting the quadratic equal to zero.
$x^(2)-2x-3=0$
Factor to find that it's equivalent to
(x-3)(x+1)=0
Therefore x is equal to positive 3 and negative 1. Plug both back into the original equation. Whichever does not work is the extraneous root, and the answer is the one that does.
$x= √(2x+3)$
$3= √(2(3)+3)$
$3= √(9)$
Extraneous root would be negative 3.

$-1= √(2(-1)+3)$
$-1= √(1)$
Extraneous root would be positive 1.

Your answers are positive 3 and negative 1.
Extraneous roots are negative 3 and positive 1.

What is the perimeter and area of the shape?

HELPPP giving 20 points

Answers

Answer:

Perimeter: 90 + 90 + 100 + 100 = 380 ft

Area: 90*90 = 8100 ft.²

Step-by-step explanation:

hope this helps! please give brainliest :)

What is the total surface area of a right circular cylinder with base radius 7cm and height 12cm.

Answers

Answer:

Using 3.14 for pi

835.24 cm^2

Using the pi button for pi

835.6636459 cm^2

Step-by-step explanation:

The surface area of a cylinder is given by

SA = 2 pi r^2 + 2 pi r h

= 2 * pi ( 7)^2 + 2 pi ( 7) * 12

= 98 pi + 168 pi

=266 pi

Using 3.14 for pi

835.24 cm^2

Using the pi button for pi

835.6636459 cm^2

Answer:

226 $\pi$ or 835.664

Step-by-step explanation:

Surface area of a right cylinder= 2πrh+2πr^2

=2π7✖️12+2π49

=226π

Hope this helped, and have a nice rest of your day!

Solve the following equation: 28 ÷ 7 + 2 × 3 = ?

A. 24B. 18C. 10D. 12

Answers

Using the helpful saying
Please (parentheses)
Excuse (exponents)
My (multiply)
Dear (divide)
Aunt (add)
Sally (subtract)

We can see that multiplying comes first in this equation, then dividing then adding so
2x3=6
then
28/7=4
then
6+4=10

So your answer is C

The length of a rectangle is 3n+ 2 and its width is n-1. The perimeter of the rectangle is twice the sum of its length and its width. write an expression that represents the perimeter of the rectangle. Find the perimeter of the rectangle when n= 4 inches

Answers

Length, L = 3n + 2
Width, W = n - 1

Perimeter, P = 2*(L + W)

   = 2*( 3n + 2 + n - 1)

   = 2*(3n + n + 2 - 1)

   = 2*(4n + 1)

   = 2*4n + 2*1

   = 8n + 2

Perimeter = (8n + 2)

Perimeter, when n = 4, 8n + 2 = 8*4 + 2 = 32 +2 = 34

Perimeter = 34 inches.

A number increased by four is the same as 19 minus 2 times the number

Answers

From the information given, 4 added to the unknown number is equal to 2 times the unknown number when it is subtracted from 19.

Let the number be x

x + 4 = 19 - 2 (x)

We now expand and simplify the equation by placing unknown on one side and the known on the other side

x + 4 = 19 - 2x

x + 2x = 19 - 4

3x = 15

x = 15 /3

x = 5

Other Questions

What integer is equivalent to93/2

A sack contains red and blue marbles. The ratio of red marbles to blue marbles is 4:3. If there are 18 blue marbles in the sack, how many red marbles are in the sack?

What is the difference of the two polynomials?(7y2 + 6xy) – (–2xy + 3) A7y2 + 4xy – 3 B7y2 + 8xy – 3 C7y2 + 4xy + 3 D7y2 + 8xy + 3

How many degrees does the hour hand move from 3:00 to 5:30?