Mathematics, 16.04.2020 02:28 dtrdtrdtrdtrdrt3415

The Highway Safety Department wants to study the driving habits of individuals. A sample of 37 cars traveling on a particular stretch of highway revealed an average speed of 70.7 miles per hour with a standard deviation of 6.3 miles per hour. Round to 4 decimal places. 1.Calculate a 90% confidence interval for the true mean speed of all cars on this particular stretch of highway

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90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].

Step-by-step explanation:

We are given that a sample of 37 cars traveling on a particular stretch of highway revealed an average speed of 70.7 miles per hour with a standard deviation of 6.3 miles per hour.

Firstly, the pivotal quantity for 90% confidence interval for the true mean is given by;

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

where, $\bar X$ = sample average speed of cars = 70.7 miles per hour

s = sample standard deviation = 6.3 miles per hour

n = sample of cars = 37

$\mu$ = true mean speed

Here for constructing 90% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.

So, 90% confidence interval for the true mean, $\mu$ is ;

P(-1.688 < t_3_6 < 1.688) = 0.90 {As the critical value of t at 36 degree of

freedom are -1.688 & 1.688 with P = 5%}

P(-1.688 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 1.688) = 0.90

P( $-1.688 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.688 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

P( $\bar X-1.688 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.688 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

90% confidence interval for $\mu$ = [ $\bar X-1.688 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+1.688 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $70.7-1.688 \times {\frac{6.3}{\sqrt{37} } }$ , $70.7+1.688 \times {\frac{6.3}{\sqrt{37} } }$ ]

= [68.9517 miles per hour , 72.4483 miles per hour]

Therefore, 90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].

The interpretation of the above interval is that we are 90% confident that the true mean speed of all cars will lie between 68.9517 miles per hour and 72.4483 miles per hour.

Answer from: Quest

2/3

step-by-step explanation:

the slope of a line is equal to the rise/run. in this case the line rises 2 units for every +3 units it moves

What is the slope of a line that is parallel to the line shown? taking quiz need

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

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