STATS HELP PLEASE

Question

E is the only one i am struggling with. How can I do it and please make it simple for me to understand. Thanks

A dishwasher has a mean lifetime of 15 years with an estimated standard deviation of 3 years. Assume the lifetime of a dishwasher is normally distributed.

a) Identify the individual, variable, and type of variable in the context of this problem.

  The individual object is Select an answer mean lifetime mean lifetime of all dishwashers lifetime all dishwashers a randomly selected dishwasher Correct

  The variable information collected from each individual is Select an answer a randomly selected dishwasher lifetime all dishwashers mean lifetime mean lifetime of all dishwashers Correct

  This variable is a Select an answer quantitative -- continuous qualitative quantitative -- discrete Correct variable.

b) What is the wording of the random variable X in the context of this problem?

  The random variable X = Select an answer the mean lifetime of a randomly selected dishwasher the mean lifetime of a randomly selected sample of dishwashers the lifetime of a randomly selected dishwasher the mean lifetime of all dishwashers Correct

c) Why can the Empirical Rule be used to approximate probabilities on this problem?

   Select an answer The Empirical Rule can only be used to approximate probabilities for problems where the random variable has a normal distribution and we can always assume the random variable has a normal distribution. The Empirical Rule can be used to approximate probabilities for any problem where there is a quantitative random variable and lifetime is a quantitative random variable. The Empirical Rule can only be used to approximate probabilities for problems where the random variable has a normal distribution. It is given in the problem that the random variable has a normal distribution. The Empirical Rule can be used to approximate probabilities for any problem where there is a qualitative random variable and lifetime is a qualitative random variable. Correct

d) Use the Empirical Rule to approximate the percentage of dishwashers that last between 12 years and 18 years.

  There is about 68Correct % of dishwashers that last between 12 years and 18 years.

e) If the warranty guarantees the dishwasher will last at least 12 years or your money back, what is the probability that the company will have to refund money to a customer?

Answer 1

Hi Bailey,

Part (e) requires the classic equation in introductory statistics:

z=x-mu/sigma

Breaking this down:

z=z-score

x=single value you are interested in

mu=mean

sigma=standard deviation

Now, we have all values we need to compute z:

x=12, the value you were asked to compute probability for

mu=15

sigma=3

Thus:

z=(12-15)/3

z=-1

Now, go to the z-table. Look in the column for -1 and the row for 0.0--it should be the first one.

Now, this is normally distributed, which means we can standardize, which means:

P(Z< -1.0)=P(X<12)

This is the probability we want--the customer gets their money back if the washer lasts less than 12 years, so:

P(Z< -1.0) =P(X<12)=0.1587

I hope this helps. Let me know if you have any questions.