Can someone show me the steps to working this problem out because i got a test on this next week? for the in advance.

a light bulb producing company states that its lights will last an average of 1200 hours with a standard deviation of 200 hours. a sample of 100 light bulbs from the company were tested and the researcher found that the average life of each light bulb was 1050 hours. at a 95% confidence level, determine whether these light bulbs are in compliance with the company's claim.

You must use the Standard Normal tables for this problem since n (100) is large. 

First find the Confidence Interval (CI), then examine if 1050 falls within the range

CI = mean +/- (z*)(standard deviation)/sqrt n 

where z* comes from the standard normal table with 5%/2 = 0.025 in each tail. 

z* = 1.96 

CI = mean +/- (z*)(standard deviation)/sqrt n 

CI = 1200 +/- (1.96)(200)/sqrt 100 

CI = 1160.8 to 1239.2 

Since 1050 DOES NOT fall within the CI, you would REJECT the hypothesis that these bulbs are in compliance. I hope this helps.

First term = a = 125

Step-by-step explanation:

Question: find the number of shoppers on the first day

This is a geometric progression question

The sum of the terms = 671

Sum of a geometric sequence,Sn = (ar^n - 1) / (r - 1)

Where,

n = number of term in the sequence.

a = first term in the sequence.

r = common ratio

r = 1 + 20%

= 1 + 20/100

= 1 + 0.2

= 1.2

n = 4 (first 4 days)

Sn = (ar^n - 1) / (r - 1)

Sn = 671 where n = 4

671 = {a × 1.2^(4) - 1} / 1.2 - 1

671 = {a × 2.0736 - 1} / 0.2

671 = (2.0736a - a) / 0.2

671 = 1.0736a / 0.2

671 = 5.368a

Divide both sides by 5.368

a = 671 / 5.368

a = 125