How is growth shown in a rule

A random sample of 10 parking meters in a resort community showed the following incomes for a day. Assume the incomes are normal

GenaCL600 [577]

Answer:

A 95% confidence interval for the true mean is [$3.39, $6.01].

Step-by-step explanation:

We are given that a random sample of 10 parking meters in a resort community showed the following incomes for a day;

Incomes (X): $3.60, $4.50, $2.80, $6.30, $2.60, $5.20, $6.75, $4.25, $8.00, $3.00.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean income = $\frac{\sum X}{n}$ = $4.70

s = sample standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$ = $1.83

n = sample of parking meters = 10

$\mu$ = population mean

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-2.262 < $t_9$ < 2.262) = 0.95 {As the critical value of t at 9 degrees of

freedom are -2.262 & 2.262 with P = 2.5%}

P(-2.262 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.262) = 0.95

P( $-2.262 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu$ < $2.262 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.262 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.262 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.262 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.262 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $4.70-2.262 \times {\frac{1.83}{\sqrt{10} } }$ , $4.70+ 2.262 \times {\frac{1.83}{\sqrt{10} } }$ ]

= [$3.39, $6.01]

Therefore, a 95% confidence interval for the true mean is [$3.39, $6.01].

The interpretation of the above result is that we are 95% confident that the true mean will lie between incomes of $3.39 and $6.01.

Also, the margin of error = $2.262 \times {\frac{s}{\sqrt{n} } }$

= $2.262 \times {\frac{1.83}{\sqrt{10} } }$ = 1.31

4 0

3 years ago

Does there appear to be a proportional relationship between the radius and circumference of a circle? Explain or show your reaso

elena-14-01-66 [18.8K]

Answer:

thx

Step-by-step explanation:

3 0

3 years ago

Faiza, Krish and Joe start cycling around the park from the same point at the same time. Faiza circles the park in 60 seconds, K

pishuonlain [190]

Answer:

The time at which they will all meet at a place together is 350 minutes

Step-by-step explanation:

The time it takes Faiza to cycle the park = 60 seconds

The time it takes Krish to cycle the park = 14 seconds

The time it takes Joe to cycle the park = 25 seconds

Therefore, the time they will all meet at a place together is given by their Lowest Common Multiple as follows;

LCM = 60 × 14 × 25 = 21,000 seconds

Therefore, the time at which they will all meet at a place together in minutes = 21000 seconds/(60)×minute/second = 350 minutes

7 0

3 years ago

Which of the following numbers is greatest, or furthest to the right on the number line? {56, 39, 74, 81, 62}

Dimas [21]

The greatest number is 81

4 0

3 years ago

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Which of the following inequalities represents "the car has no more than 5 gallons of gas left in the gas tank"?

MrRissso [65]

The answer is B. Hope this helps :)

7 0

3 years ago

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