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Nesterboy [21]
3 years ago
14

A superstar major league baseball player just signed a new deal that pays him a record amount of money. The star has driven in a

n average of 110 runs over the course of his career, with a standard deviation of 31 runs. An average player at his position drives in 80 runs. What is the probability the superstar bats in fewer runs than an average player next year? Assume the number of runs batted in is normally distributed.

Mathematics
1 answer:
Likurg_2 [28]3 years ago
8 0

Answer:

  about 16.7%

Step-by-step explanation:

An appropriate probability calculator can tell you the probability of being below 80 for the given normal distribution. The calculator shown below says it is about 0.167.

__

The corresponding z-value is ...

  (x -μ)/σ = (80 -110)/31 = -30/31 ≈ -0.9677

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The average annual premium for automobile insurance in the United States is $1411. A representative sample of annual premiums fo
Harrizon [31]

Using confidence interval concepts, it is found that:

a) The point estimate is the sample mean.

b) The confidence interval is: \overline{x} \pm T\frac{s}{n}

c) If $1411 is between the bounds of the interval yes, otherwise no.

--------------

  • At item a, it asks to provide a point estimate for the population mean, which is the sample mean \overline{x}

--------------

Item b:

  • In the spreadsheet, it is possible to find the <em>standard deviation for the sample</em>, thus, the t-distribution is used.
  • The confidence interval will be given by:

\overline{x} \pm T\frac{s}{n}

In which:

  • \overline{x} is the sample mean.
  • T is the critical value, from the t-distribution, with a two-tailed area of \frac{1 - 0.95}{2} = 0.025 and n-1 degrees of freedom.
  • s is the standard deviation for the sample.
  • n is the sample size.

--------------

Item c:

We have to check if 1411 is between \overline{x} - T\frac{s}{n} and \overline{x} +T\frac{s}{n}.

  • If it is, the interval includes the National Average, otherwise, it does not.

A similar problem is given at brainly.com/question/24232455

7 0
3 years ago
Bianca uses 1/3 of clay to make 4 bowls. She uses the same amount of clay for each bowl. How much clay does Bianca use for each
kkurt [141]

Answer:

1/12clay each bowl

Step-by-step explanation:

Since we know she used 1/3, simply divide 1/3 by 4 to get your answer.

1/3 / 4/1

1/3 * 1/4

1/12

8 0
3 years ago
The perimeter of an equilateral triangle is 63 inches. If the length pf each side is (4x-3), write an equation and find the valu
Nady [450]

Answer:

x = 6

Step-by-step explanation:

Givens

There are 3 sides. All are equal to (4x - 3)

Their sum = 63

Formula

3(4x - 3) = 63

Solution

  • 3(4x - 3) = 63            Divide by 3
  • 12x - 9 = 63               Add 9 to both sides
  • 12x = 63 + 9    
  • 12x = 72                    Divide by 12
  • x = 72/12

x = 6                          Answer  

7 0
3 years ago
Leon charge $75 at an interest rate of 12.5% how much Will Leon have to pay after one month if he makes no payments
Fudgin [204]
Multiply the $75 by 1.125 which represents the total amount of interest AND the orgininal amount
75*1.125=$84.37
3 0
3 years ago
Help center of circle
Lelu [443]

Answer:

Center = (7, - 5)

Radius = 3

Step-by-step explanation:

{x}^{2}  +  {y}^{2}  + 14x - 10y + 65 = 0 \\  {x}^{2}  + 14x +  {y}^{2}  - 10 + 65 = 0 \\ ( {x}^{2}  + 14x +  {7}^{2})  -  {7}^{2}  +  ({y}^{2}  - 10y +  {5}^{2})  \\-  {5}^{2}  + 65 = 0 \\ (x + 7)^{2}  + (y - 5)^{2}  - 49 - 25 + 65 = 0 \\  (x + 7)^{2}  + (y - 5)^{2}  - 49  + 40= 0 \\   (x + 7)^{2}  + (y - 5)^{2}  - 9= 0 \\   (x + 7)^{2}  + (y - 5)^{2}   =  9 \\  (x + 7)^{2}  + (y - 5)^{2}   =   {3}^{2}  \\  equating \: it \: with \: \\ (x  -  h)^{2}  + (y - k)^{2}   =   {r}^{2}  \\  - h = 7 \implies \: h =  - 7 \\  - k =  - 5 \implies \: k = 5 \\ center = ( - h, \:  - k)  = (7, \:  \:  - 5) \\  \\ radius \: r = 3

7 0
4 years ago
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