The age of customer for a particular retail stone follows a normal distribution with a mean of 37.5 years and standard deviation of 15 years . given that the sample size is 36
A computer standard error?
B what is the probability that the next customer who enters
the store will be more than 31 years old?
C what is the probability that the next customer who enters the store will be less than 42 years old?
A) The standard error can be calculated using the formula:
SE = σ/√n
where σ is the standard deviation, n is the sample size.
SE = 15/√36 = 2.5
Therefore, the standard error is 2.5.
B) The z-score can be calculated using the formula:
z = (x - μ) / SE
where x is the value we want to find the probability for, μ is the mean, and SE is the standard error.
z = (31 - 37.5) / 2.5 = -2.6
Using a standard normal distribution table or calculator, the probability of getting a z-score of -2.6 or less is 0.0047.
Therefore, the probability that the next customer who enters the store will be more than 31 years old is 1 - 0.0047 = 0.9953 or approximately 99.53%.
C)
z = (42 - 37.5) / 2.5 = 1.8
Using a standard normal distribution table or calculator, the probability of getting a z-score of 1.8 or less is 0.9641.
Therefore, the probability that the next customer who enters the store will be less than 42 years old is 0.9641 or approximately 96.41%.