The lifetime (in hours) of a 60-watt light bulb is a random variable that has a normal distribution with σ = 30 hours. a random sample of 25 bulbs put on test produced a sample mean lifetime of = 1038 hours. if in the study of the lifetime of 60-watt light bulbs it was desired to have a margin of error no larger than 6 hours with 99% confidence, how many randomly selected 60-watt light bulbs should be tested to achieve this result?

They must have about 166 randomly 60 watt light bulbs to achieve the result

N = 166

Explanation:

σ = 30

% 99 = 2.576

Using the standard equation of statistics knowing the difference between the measurement have a margin error no larger than 6 can solve

σ = √∑ ( x - z' )²  / N

Solve to N

N = ( % * σ  / Δ x  ) ²

N = ( 2.576 * 30 / 6 )²

N = 12.88 ²

N = 165. 89 44 ≅ 166

the answer is to check all of them! they all apply well at least i think so!

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.