According to the latest real estate report from a suburban town, the mean number of home purchases during last quarter was 175 homes with a population standard deviation of 6 homes. A real estate agent believes that the recent increase of mortgage interest rates is causing a decline in home purchases. To test this, the real estate agent randomly selects 60 recent home purchases. What is the probability that the mean of this sample of home purchases is between 173 and 174 homes

Answer:

The probability that the mean of this sample of home purchases is between 173 and 174 homes

P(173≤X≤174) = 0.0936

Step-by-step explanation:

Step(i):-

Given that the mean of the Population = 175

Given that the standard deviation of the Population = 6

Let 'x⁻' be the mean of the random sample

Given that  x₁⁻ = 173

[tex]Z_{1} = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{173-175}{\frac{6}{\sqrt{60} } } =-2.58[/tex]

Given that  x₂⁻ = 174

[tex]Z_{2} = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{174-175}{\frac{6}{\sqrt{60} } } = -1.29[/tex]

Step(ii):-

The probability that the mean of this sample of home purchases is between 173 and 174 homes

P(X₁≤X≤X₂)      = P(Z₁≤Z≤Z₂)

                       = P(Z≤Z₂) - P(Z≤Z₂)        ( both values 'Z' values are negative)

                       = 0.5 -A(Z₁) - (0.5 -A(Z₂))

                      = |A(Z₂) -A(Z₁)|

P(173≤X≤174)     =   | A(2.58)-A(1.29)|

                  = 0.4951 - 0.4015       (∵ from normal table)

                = 0.0936

Final answer:-

The probability that the mean of this sample of home purchases is between 173 and 174 homes

P(173≤X≤174) = 0.0936

helpppp pleaseee????

if h(x)=3^x then h (-4) =

PLEASE ANSWER THIS ASAP I WILL MARK YOU THE BRAINLIEST
SHOW YOUR WORK!!!
Calculate the volume of the following three-dimensional object

Kim is repainting a storage trunk shaped like a rectangular prism as shown.

Kim will paint all the faces of the outside of the storage trunk when it is closed. How many square feet will Kim paint?

I need help with this
[tex] \sqrt[3]{4} \times \sqrt{3} [/tex]
25 points.​

Find the value of x in the triangle shown below. ​

Your parents gave you $0.35 on Sunday and then gave you twice as much money on Monday as they did on Sunday. On Tuesday, they gave you twice as much money as they gave you monday. The pattern continued for a week. How much money did your parents give you on Saturday??

A function, f(x),represents the height of a plant x months after being planted. Students measure and record the height on a
Select the appropriate domain for this situation.
OA.
the set of all real numbers
OB.
the set of all integers
O c.
the set of all positive integers
OD
the set of all positive real numbers

What is the area?
O 90 square kilometers
O 45 square kilometers
O 27 square kilometers
O 36 square kilometers

plz help me please please​

HURRY! ANSWER QUICK PLEASEEE

a cylinder with the radius of 12 feet and height of 1.2 feet. What is the total surface area of the cylinder in square feet?

Elena is graduating from high school. She will attend a private, 4-year university and study to become a Certified Public Accountant. The annual cost for her tuition, room and board, and books is $22,255. Elena's parents have a college fund with $ 54,000 to help with the costs. Elena received a scholarship for $500 per semester for four years .

A local charity receives 1/3 of funds raised during a craft fair and a bake sale. The total amount given to the charity was $137.45. How much did the bake sale raise?

(NEED ANSWER ASAP!!)

is it possible to have the ordered number pair 3;7 on the graph​

Slove the system of linear equations by graphing y=-x+7 y=x-1

Simplify w x 12 x 3
Helppp

Drag each sign or value to the correct location on the equation. Each sign or value can be used more than once, but not all signs and values will
be used.
The focus of a parabola is (-4,-5), and its directrix is y=-1. Fill in the missing terms and signs in the parabola's equation in standard form.

Neil is going to a bookstore 45 miles away. The bridge was closed on the way back, so
he had to take an alternate route and had to drive 15 mph slower, which make the trip
back take 7 minutes longer. How fast was he going on the way to the bookstore?

A right prism has a volume of 65 cubic inches. The prism is enlarged so its height is increased by a factor of 20, but the other dimensions do not change. What is the new volume? A. 1000in.3 B. 1300in.3 C. 1200in.3 D. 1100in.3

Vincent paints 75% of his statues. He paints 60 statues. How many statues does Vincent have in total?

Plz Help me this is already overdue

Select 2A316 in base 10.

3 of the 100 digital video recorders​ (DVRs) in an inventory are known to be defective. What is the probability you randomly select an item that is not​ defective?

What is the volume of a sphere with a radius of 60.5 ft, rounded to the nearest tenth
of a cubic foot?

Tamika is making a flag design in the shape of a parallelogram. Which x- and y-values must she use in order to guarantee that the flag is in the shape of a parallelogram?​

Michelle counted 40 green cars and 20 silver cars in the parking lot. If
the number of green cars stays the same, how many more silver cars
would need to be added so the ratio of green cars to silver cars is 1 to 3?

8[x-y] use x=5 and y=2

Identify the figure, name the bases,faces,edges, and vertices

What is the mode of the data set? {32, 29, 35, 25, 32, 22, 30} Enter your answer in the box.