The average lifetime of smoke detectors that a company manufactures is 5 years, or 60 months, and the standard deviation is 8 months. find the probability that a random sample of 30 smoke detectors will have a mean lifetime between 58 and 63 months

0.8945

Step-by-step explanation:

Let x represents the lifetime of smoke detectors that a company manufactures.

We assume that the lifetime of smoke detectors that a company manufactures is normally distributed.

Given : The average lifetime of smoke detectors that a company manufactures is 5 years, or 60 months, and the standard deviation is 8 months.

i.e.

Sampl siez : n= 30

Then, the probability that a random sample of 30 smoke detectors will have a mean lifetime between 58 and 63 months will be :-

Hence, the probability that a random sample of 30 smoke detectors will have a mean lifetime between 58 and 63 months= 0.8945

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;