Alight bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 753 hours. a random sample of 28 light bulbs has a mean life of 726 hours. assume the population is normally distributed and the population standard deviation is 64 hours. at alphaequals0.05, do you have enough evidence to reject the manufacturer's claim?

P (z for -2.23)  is -0.9871

Step-by-step explanation:

Given data

mean life x = 753 hours

sample n = 28

mean  y = 726

standard deviation SD = 64 hours

to find out

check to have enough evidence to reject his claim

solution

we know that given mean is x ≥ 753

we found mean = 726

so difference =  y - x  = 726 - 753 = -27

and we know σ = SD/√n = 64 / √28 = 12.094896

Z  =  y - x /  σ

Z  =  -27 /  12.09

Z = -2.23

so probability value

P (z for -2.23)  is -0.9871

so z value is less than alpha = 0.05

so reject

so this is enough evidence to reject his claim

step-by-step explanation:

there are 36 inches in a yard

25 : 36 = 0.69 yards (you can round to 0.70)

part a: 1.08

part b: 27.59