Answer:
a. 1200hours
b. σ² = 400² =160000hour
c. standard error = 133.33
d. for 9 lightbulb it is likely that 9*0.146 = 1.31 bulbs will have lives of fewer than 1,050 hours?
Step-by-step explanation:
mean of 1,200 hours
σ, a standard deviation of 400 hours.
Sample size, N = nine bulbs,
a) mean of the sample mean lifetime: is given as 1,200 hours
b) variance of the sample mean is the square of the σ, a standard deviation of 400 hours.
σ² = 400² =160000hours
c) What is the standard error of the sample mean?
The standard deviation of a sampling distribution of mean values is called the standard error of the means,
standard error of the means, σx = σ √N
The formula for the standard error of the means is true for all values infinite number of sample, N.
σx = σ √N
=400 √9 = 400/3 =133.3333
d) the probability that, on average, those nine lightbulbs have lives of fewer than 1,050 hours
The area under part of a normal probability curve is directly proportional to probability and the value is calculated as
z = ( x₁−x) /σ
where z = propability of normal curve
x₁ = variate mean = 1050hours
x = mean of 1200hours
σ = standard deviation = 400
applying the formula,
z= (1050-1200)/400
z = 150/400 =0.375
Using a table of partial areas beneath the standardized normal curve (see Table of normal curve, a z-value of 0.375 corresponds to an area of 0.1460 between the mean value.
Thus the probability of a lightbulbs having lives of fewer than 1,050 hours is 0.1460.
for 9 lightbulb it is likely that 9*0.146 i.e. 1.31 bulbs will have lives of fewer than 1,050 hours?
