Life tests performed on a sample of 13 batteries of a new model indicated:

(1) an average life of 75 months, and

(2) a standard deviation of 9 months. other battery models, produced by similar processes, have normally distributed life spans. the 90% confidence interval for the population mean life of the new model is:

The 90% confidence interval would be given by (70.557;79.443)  

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

represent the sample mean  

population mean (variable of interest)  

s=9 represent the sample standard deviation  

n=13 represent the sample size  

Calculate the confidence interval

The confidence interval for the mean is given by the following formula:  

(1)  

In order to calculate the critical value we need to find first the degrees of freedom, given by:  

Since the confidence is 0.90 or 90%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,12)".And we see that .

Now we have everything in order to replace into formula (1):  

So on this case the 90% confidence interval would be given by (70.557;79.443)  

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

step-by-step explanation: