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Lady bird [3.3K]
3 years ago
14

The commute time to work in the U.S. Has a bell shaped distribution with a population mean of 24.4 minutes and a population stan

dard deviation of 6.5 minutes. What proportion of the population has a commute time: a) between 11.4 minutes and 37.4 minutes? (1 pt) b) less than 11.4 minutes? (1 pt) c) greater than 37.4 minutes? (1 pt)
Mathematics
1 answer:
Alexxx [7]3 years ago
5 0

Answer:

1. 0.9544

2. 0.0228

3. 0.0228

Step-by-step explanation:

The computation is shown below;

As we know that

At Normal distribution

P(X < A) = P(Z < \frac{(A - mean)}{standard deviation})

As per the question, the data provided is as follows

Mean = 24.4 minutes

Standard deviation = 6.5 minutes

Based on the above information

P(11.4 < X < 37.4) = P(X < 37.4) - P(X < 11.4)

= P(Z < (37.4 - 24.4) ÷ 6.5) - P(Z < (11.4 - 24.4) ÷ 6.5)

= P(Z < 2) - P(Z < -2)

= 0.9772 - 0.0228

= 0.9544

2. P(X < 11.4) = 0.0228

3. P(X ≥ 37.4) = 1 - P(X < 37.4)

= 1 - 0.9772

= 0.0228

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If the sale tax rate is 8.75% in New York State, how much sales tax would you pay for a $35 pair of pants? And at Best Buy they
bogdanovich [222]

The pants are $38.06 and the television is $1,147.50.

The sales tax on the pair of pants is calculated by multiplying $35 x .0875 = $3.06

The total cost is $35 + 3.06 = $38.06.

The sales price of the television is calculated by multiplying $1,250 x .85, (100 - .15 discount = .85) = $1,062.50 is the sales price

The sales tax is calculated by multiplying $1,062.50 x .08 = $85

The total price is $85 + $1,062.50 = $1,147.50

7 0
3 years ago
If my diameter is 19 inches what is my radius​
Masja [62]

Answer:

38

Step-by-step explanation:

To find the radius of a circle you multiply the diameter by 38

(to find the diameter, you divide the radius by 2)

4 0
3 years ago
Please help very urgent
Alik [6]

Answer:

32, <u>16</u>, <u>8</u>, <u>4</u>, <u>2</u>, 1

Explanation:

The geometric mean can be represented by \sqrt[n]{x_{1} • x_{2} • x_{3} • .. x_{n}}.

Which is the mean of the product of n numbers, used to find the average of a geometric progression.

Don't get confused by geometric mean, it is only asking you about the next numbers in the geometric sequence given the first and sixth term.

The explicit rule for a geometric sequence can be modeled by:

a_{n} = a_{1} • r^{n-1}

Where a_{n} is the nth term, a_{1} is the first term in the sequence, n is the term number, and r is the common ratio.

Since we already know the first term, a_{1} will simply be 32.

Since we know it's geometric, there will be an exponential relationship, which means that we will use the geometric mean to find the common ratio.

There are 6 total terms, r is raised to the n – 1 so 6 – 1 = 5, and that will be the degree of this root.

\sqrt[5]{\frac{a_{6}}{a_{1}}} =

\sqrt[5]{\frac{1}{32}} =

\frac{1}{2}.

Therefore: r = \frac{1}{2}.

Using all the information we have, we can find the explicit rule:

a_{n} = a_{1} • r^{n-1}

  • a_{1} = 32
  • r = \frac{1}{2}

a_{n} = a_{1} • r^{n-1} →

\boxed{a_{n} = 32 • (\frac{1}{2})^{n-1}}

________________________________

We can test that this works by substituting the number location of the term you want to find.

For instance:

a_{1} = 32 • (\frac{1}{2})^{1-1}

a_{1} = 32 • (\frac{1}{2})^{0}

a_{1} = 32 • 1

a_{1} = 32

a_{6} = 32 • (\frac{1}{2})^{6-1}

a_{6} = 32 • (\frac{1}{2})^{5}

a_{6} = 32 • \frac{1}{32}

a_{6} = 1

3 0
2 years ago
Read 2 more answers
Math... please help :(
NeX [460]
B! Sorry if im wrong..:(
8 0
2 years ago
Read 2 more answers
Gideon is painting all sides of a square pyramid-shaped decoration at the top of his fence post. A net of the decoration is show
frez [133]
Gideon is painting all sides thus we find the overall area of the square pyramid given in the picture. A square pyramid is a polyhedron that consists of a square and 4 triangles. To solve the area that Gideon will have to paint, we can calculate the area of the square and the area of the triangles then add these two values of area. We proceed as follows:
Area of the square = s^2 where s is the measure of the side
Area of the square = 4^2 = 16 in^2

Area of the triangle= 1/2 bh where b is the base of the triangle and h is height of the triangle
Area of the triangle = 1/2 (4) (5) = 10 in^2
We multiply the area of the triangle to four in order to obtain the total area of the triangles.
Total area of the triangles = 4 x 10 = 40 in^2

We then add the two areas,
Total Area = 16 + 40 = 56 in^2

Thus the total area that Gideon will have to paint for one square pyramid is 56 in^2.
6 0
3 years ago
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