A dishwasher has a mean lifetime of 12 years with an estimated standard deviation of 1.25 years. The lifetime of a dishwasher is normally distributed. Suppose you are a manufacturer and you take a sample of 15 dishwashers that you made. It is possible with rounding for a probability to be 0.0000. a) Identify the individual, variable, type of variable and the random variable X in the context of this problem. The individual is Select an answer 15 randomly selected dishwashers the lifetime a randomly selected dishwasher the mean lifetime of all dishwashers all dishwashers the mean lifetime of 15 randomly selected dishwashers The variable information collected from each individual is Select an answer the mean lifetime of all dishwashers the lifetime 15 randomly selected dishwashers the mean lifetime of 15 randomly selected dishwashers all dishwashers a randomly selected dishwasher This variable is a Select an answer qualitative -- discrete quantitative -- continuous qualitative variable. The random variable X is as follows: Select an answer rv X = the mean lifetime of all dishwashers rv X = all dishwashers rv X = the mean lifetime of 15 randomly selected dishwashers rv X = the lifetime of a randomly selected dishwasher rv X = a randomly selected dishwasher rv X = lifetime is normally distributed b) List the givens with the correct symbols. ? μ σ X̄ n s N p X = 12 years ? X̄ n σ s X μ p N = 1.25 years ? p X σ X̄ μ N n s = 15 c) Identify the random variable ¯¯¯XX¯ in the context of this problem. Select an answer rv X̄ = lifetime is normally distributed rv X̄ = the lifetime of a randomly selected dishwasher rv X̄ = a randomly selected dishwasher rv X̄ = the mean lifetime of all dishwashers rv X̄ = the mean lifetime of 15 randomly selected dishwashers rv X̄ = the lifetime of 15 randomly selected dishwashers
A dishwasher has a mean lifetime of 12 years with an estimated standard deviation of 1.25 years. The lifetime of a dishwasher is
It is possible with rounding for a probability to be 0.0000.
a) Identify the individual, variable, type of variable and the random variable X in the context of this problem.
The individual is Select an answer 15 randomly selected dishwashers the lifetime a randomly selected dishwasher the mean lifetime of all dishwashers all dishwashers the mean lifetime of 15 randomly selected dishwashers
The variable information collected from each individual is Select an answer the mean lifetime of all dishwashers the lifetime 15 randomly selected dishwashers the mean lifetime of 15 randomly selected dishwashers all dishwashers a randomly selected dishwasher
This variable is a Select an answer qualitative -- discrete quantitative -- continuous qualitative variable.
The random variable X is as follows:
Select an answer rv X = the mean lifetime of all dishwashers rv X = all dishwashers rv X = the mean lifetime of 15 randomly selected dishwashers rv X = the lifetime of a randomly selected dishwasher rv X = a randomly selected dishwasher rv X = lifetime is normally distributed
b) List the givens with the correct symbols.
? μ σ X̄ n s N p X = 12 years
? X̄ n σ s X μ p N = 1.25 years
? p X σ X̄ μ N n s = 15
c) Identify the random variable ¯¯¯XX¯ in the context of this problem.
Select an answer rv X̄ = lifetime is normally distributed rv X̄ = the lifetime of a randomly selected dishwasher rv X̄ = a randomly selected dishwasher rv X̄ = the mean lifetime of all dishwashers rv X̄ = the mean lifetime of 15 randomly selected dishwashers rv X̄ = the lifetime of 15 randomly selected dishwashers
d) Find the mean of the sampling distribution of the sample mean.
Put the numeric value in the first box and the correct units in the second box.
e) Find the standard deviation of the sampling distribution of the sample mean.
Put the numeric value rounded to two decimal places in the first box and the correct units in the second box.
f) What is the shape of the sampling distribution of the sample mean?
Select an answer normal or approximately normal unknown right-skewed left-skewed uniform
Why? Check all that apply:
- n is less than 30
- σσ is known
- n is at least 30
- population is not normal
- population is normal
- σσ is unknown
g) Find the probability that the sample mean lifetime of the 15 randomly selected dishwashers is less than 12.2 years.
Round final answer to 4 decimal places.
DO NOT use the rounded standard deviation from part e in this computation.
Use the EXACT value of the standard deviation with the square root.
h) Find the probability that the sample mean lifetime of the 15 randomly selected dishwashers is less than 11.4 years.
Round final answer to 4 decimal places.
DO NOT use the rounded standard deviation from part e in this computation.
Use the EXACT value of the standard deviation with the square root.
i) Is a mean lifetime of 11.4 years unusually low for 15 randomly selected dishwashers?
Select an answer Yes, the probability of having a sample mean lifetime of at least 11.4 years is less than or equal to 0.05 Yes, the probability of having a sample mean lifetime of at least 11.4 years is more than 0.05 Yes, the probability of having a sample mean lifetime of at most 11.4 years is less than or equal to 0.05 Yes, the probability of having a sample mean lifetime of at most 11.4 years is more than 0.05 No, the probability of having a sample mean lifetime of at least 11.4 years is less than or equal to 0.05 No, the probability of having a sample mean lifetime of at least 11.4 years is more than 0.05 No, the probability of having a sample mean lifetime of at most 11.4 years is less than or equal to 0.05 No, the probability of having a sample mean lifetime of at most 11.4 years is more than 0.05
j) If you found a mean lifetime for a sample of 15 dishwashers as low as 11.4 years, what might you conclude?
Select an answer There is evidence that the mean lifetime of all dishwashers may now be lower than 12 years There is evidence that the mean lifetime of all dishwashers may now be higher than 12 years There is no evidence that the mean lifetime of all dishwashers has changed from 12 years
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