Mathematics, 18.08.2020 18:01 kelenski4

You measure 46 watermelons' weights, and find they have a mean weight of 60 ounces. Assume the population standard deviation is 8.5 ounces. Based on this, construct a 99% confidence interval for the true population mean watermelon weight. Give your answers as decimals, to two places.

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Answer from: levon15

A 99% confidence for the true population mean watermelon weight is [56.77 ounces, 63.23 ounces] .

Step-by-step explanation:

We are given that you measure 46 watermelons' weights, and find they have a mean weight of 60 ounces.

Assume the population standard deviation is 8.5 ounces.

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

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{} n} }$ ~ N(0,1)

where, $\bar X$ = sample mean weight = 60 ounces

$\sigma$ = population standard deviation = 8.5 ounces

n = sample of watermelons = 46

$\mu$ = population mean watermelon weight

Here for constructing a 99% confidence interval we have used a One-sample z-test statistics because we know about the population standard deviation.

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.58 < N(0,1) < 2.58) = 0.99 {As the critical value of z at 0.5% level

of significance are -2.58 & 2.58}

P(-2.58 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{} n} }$ < 2.58) = 0.99

P( $-2.58 \times {\frac{\sigma}{\sqrt{} n} }$ < ${\bar X-\mu}$ < $2.58 \times {\frac{\sigma}{\sqrt{} n} }$ ) = 0.99

P( $\bar X-2.58 \times {\frac{\sigma}{\sqrt{} n} }$ < $\mu$ < $\bar X+2.58 \times {\frac{\sigma}{\sqrt{} n} }$ ) = 0.99

99% confidence interval for $\mu$ = [ $\bar X-2.58 \times {\frac{\sigma}{\sqrt{} n} }$ , $\bar X+2.58 \times {\frac{\sigma}{\sqrt{} n} }$ ]

= [ $60-2.58 \times {\frac{8.5}{\sqrt{46} } }$ , $60+2.58 \times {\frac{8.5}{\sqrt{46} } }$ ]

= [56.77 ounces, 63.23 ounces]

Therefore, a 99% confidence for the true population mean watermelon weight is [56.77 ounces, 63.23 ounces] .

Answer from: Quest

here you hope this .

step-by-step explanation:

hypotenuse = √(15² + 8²)

= √(225 +64)

= √(289) = 17

sin(x) = cos(y) = 8/17

they are identical so long as you are doing the sine of one angle and the cosine of the only other angle that isn't the right angle.

Hurry need your use the image below to answer the following question. find the value of sin x° and

Answer from: Quest

income. 10x+1300

expenses 3x+(1800+1500)

expenses 3x+3300

to break even:

income = expense,

10x + 1300 = 3x + 3300,

solve for x.

step-by-step explanation:

mark brainliest

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You measure 46 watermelons' weights, and find they have a mean weight of 60 ounces. Assume the popul...