# Normal Distribution Question

#### Janu42

Reviewing for a class, kinda confused how to tackle this.

George and Julia both work for the campus coffee shop. Sales are slow and management is considering letting one of them go. To decide which employee to keep, each is timed on 8 independent trials of making a double decaf skim milk latte. If the sample mean times differ by more than 12 seconds, the person with the larger sample mean will be let go; otherwise both will be kept. The standard deviation of the time it takes each person to make a double decaf skim latte is known to be 10 seconds and the preparation time is found to follow a normal distribution. If the mean times for both George and Julia are actually the same, what is the probability that George will be let go?

So the null hypothesis is that both means are the same, and H1 is that George's is higher? And I have to find the probability of a type 1 error right? (The probability the null hypothesis is rejected when it is true?) And do it with sample mean of 12 greater than Julia's?

#### matheagle

MHF Hall of Honor
There's no hypothesis testing here.....

$$\displaystyle P(\bar G-\bar J>12)$$

$$\displaystyle =P\left({\bar G-\bar J-(\mu-\mu)\over \sqrt{{100\over 8}+{100\over 8}}}>{12-(0)\over 5}\right)$$

$$\displaystyle =P\left(Z>2.4\right)$$

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Janu42

#### Janu42

OK thanks, I guess I got confused when I saw the "what is the probability that George will be let go?" and misconstrued it as a type of error. Thanks

#### matheagle

MHF Hall of Honor
OK thanks, I guess I got confused when I saw the "what is the probability that George will be let go?" and misconstrued it as a type of error. Thanks

That's because you're thinking of George Constanza.