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inessss [21]
2 years ago
10

The owners of a baseball team are building a new baseball field for their team and must determine the number of seats to include

. The average game is attended by 6,500 fans, with a standard deviation of 450 people. Suppose a random sample of 35 games is selected to help the owners decide the number of seats to include. Identify each of the following and be sure to round to the nearest whole number:
Provide your answer below:
μ =------------
μx=-----------
σx=-----------
σ=------------
n=------------
Mathematics
1 answer:
lilavasa [31]2 years ago
4 0

Answer:

μ = 6500

μx= 6500

σx= 76

σ= 450

n= 35

Step-by-step explanation:

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 game is attended by 6,500 fans, with a standard deviation of 450 people.

This means that \mu = 6500, \sigma = 450

35 games:

This means that n = 35

Distribution of the sample mean:

By the Central Limit Theorem, we have \mu_x = \mu = 6500 and the standard deviation is:

\sigma_x = \frac{450}{\sqrt{35}} = 76

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Answer:

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Step-by-step explanation:

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to find out

the future value, S(t)

principal when Donna's account will be 1 million dollars when she retires in 40 year

at what rate Donna's account will have a balance of 1 million dollars in 40 years

solution

we know compounded continuously formula i.e.

amount = principal × e^{rt}    ..................1

put the value principal and rate in equation 1 to find amount any time

amount = principal × e^{rt}

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in 2nd part we have time 40 year and amount 1 million so put rate amount and time in equation 1  to find principal

rt = 0.08 × 40 = 3.2

amount = principal × e^{rt}

1000000 = principal × e^{3.2}

principal = 1000000 / e^{3.2}

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amount = principal × e^{rt}

1000000 = 2500 × e^{40r}

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40 r = ln 400

r = ln (400) / 40

r = 0.149787

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