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Fudgin [204]
3 years ago
5

The average ticket price for a Spring Training baseball game is $32.61, with a standard deviation of $8.62. In a random sample o

f 40 Spring Training tickets, find the probability that the mean ticket price exceeds $35. (Round your answer to three decimal places)
Mathematics
1 answer:
stiv31 [10]3 years ago
7 0

Using the normal probability distribution and the central limit theorem, it is found that there is a 0.04 = 4% probability that the mean ticket price exceeds $35.

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

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

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

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.  

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

The average ticket price for a Spring Training baseball game is $32.61, with a standard deviation of $8.62.

This means that \mu = 32.61, \sigma = 8.62

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

Sample of 40:

This means that n = 40, s = \frac{8.62}{\sqrt{40}}

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

In a random sample of 40 Spring Training tickets, find the probability that the mean ticket price exceeds $35.

This is 1 subtracted by the p-value of Z when X = 35, so:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{35 - 32.61}{\frac{8.62}{\sqrt{40}}}

Z = 1.754

Z = 1.754 has a p-value of 0.96.

1 - 0.96 = 0.04

0.04 = 4% probability that the mean ticket price exceeds $35.

A similar question is given at brainly.com/question/24342706

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SVETLANKA909090 [29]

Answer:

a.) April has 30 days

If you for option No.2, you would have:

[day, amount($)]

1, 0.01

2, 0.02

3, 0.04

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5, 0.16

6, 0.32

7, 0.64

8, 1.28

9, 2.56

10, 5.12

11, 10.24

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14, 81.82

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18, 1310.72

19, 2621.44

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21, 10,485.76

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24, 83,886.08

25, 167,772.16

26, 335,544.32

27, 671,088.64

28, 1,342,177.28

29, 2,684,354.56

30, 5,368,709.12

Option 2 grants you more than 5 times as much as Option A and is therefore obviously better.

b.) A diagram would show first a slow rise, than a steeper and steeper rise, then would almost growvertically. exponential growth

#coronatime

The most elegant form to describe the given numbers would simply be

$=1*2^x

You start with one, eich doubles after a day (x=1). x is the number of days and how often you multiply by 2

c.) Wasn't sure without calculating, but I guessed Opt.2, because it seemed that one should be tricked into choosing Opt.1

Have a nice day

Brainliest would be appreciated

If there are questions left, feel free to ask them

4 0
3 years ago
Please help 15 points and brainlsiet for good answer please and thank u
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3 years ago
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aniked [119]

Answer:

C = -30

Step-by-step explanation:

C = 5/9 (F - 32)

C = 5/9 ( - 22 - 32)

C = 5/9 ( -54)

C = -30

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3 years ago
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kari74 [83]

Answer:

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3 0
3 years ago
The volume of a cone is 3πx3 cubic units and its height is x units. Which expression represents the radius of the cone’s base, i
dalvyx [7]

Answer:

<em>r=3x</em>

Step-by-step explanation:

<u>The Volume of a Cone</u>

The volume of a cone of radius r and height h is:

\displaystyle V=\frac{1}{3}\pi hr^2

We are given the volume of a cone is

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Equating:

\displaystyle \frac{1}{3}\pi hr^2=3\pi x^3

Multiplying by 3:

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Simplifying by pi:

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Since h=x:

xr^2=9 x^3

Dividing by x:

r^2=9 x^2

Taking square roots:

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5 0
3 years ago
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