Mathematics, 06.05.2020 18:09 sierraaasifuent

In a random sample of 41 criminals convicted of a certain crime, it was determined that the mean length of sentencing was 51 months, with a standard deviation of 11 months. Construct and interpret a 95% confidence interval for the mean length of sentencing for this crime.

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Answer from: daniellcharmaine

95% confidence interval for the mean length of sentencing for this crime is [47.53 months , 54.47 months].

Step-by-step explanation:

We are given that in a random sample of 41 criminals convicted of a certain crime, it was determined that the mean length of sentencing was 51 months, with a standard deviation of 11 months.

Firstly, the pivotal quantity for 95% 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 length of sentencing = 51 months

= sample standard deviation = 11 months

n = sample of criminals = 41

$\mu$ = population mean length of sentencing

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

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

P(-2.021 < t_4_0 < 2.021) = 0.95 {As the critical value of t at 40 degree of

freedom are -2.021 & 2.021 with P = 2.5%}

P(-2.021 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.021) = 0.95

P( $-2.021 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $-2.021 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.021 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.021 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.021 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.021 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $51-2.021 \times {\frac{11}{\sqrt{41} } }$ , $51+2.021 \times {\frac{11}{\sqrt{41} } }$ ]

= [47.53 , 54.47]

Therefore, 95% confidence interval for the mean length of sentencing for this crime is [47.53 months , 54.47 months].

Answer from: Quest

d. is the correct answer

step-by-step explanation:

Answer from: Quest

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

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