9.2 An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780 hours, find a 96% confidence interval for the population mean of all bulbs produced by this firm.

765,795 = 96%

Step-by-step explanation:

confidence interval = 0.04  

The Za/2 theorem = 1/2 = 0.04/2 = 0.02= /x = 720z

If ; 0.02 = 2.05  then the interval is 780-2.05 x 40/√30 x 780+2.05 x 30/√30 = 765,795 = 96%

We see 40/ √30 which is found in equation of finding the sample mean at point /x = 720z

σ 40/ n√30 = 7.3029674334 and is simply a fraction of /x 720z

By normal distribution we find

The 96% confidence interval for the population mean of all bulbs = 765,795

As 765, x 1.04 = 795 = 765, 795

To find Sampling mean.

The Sampling Distribution of the Sample Mean. If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is μ (mu) and the population standard deviation is σ (sigma) then the mean of all sample means (x-bars) is population mean μ (mu).

Confidence Levelz*-value

80%1.28

90%1.645 (by convention)

95%1.96

96% 2.05

98%2.33

99%2.58

(w – 2.5)(w + 2.5)

(–4v – 9)(–4v + 9)

step-by-step explanation:

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.