Calculating Z-Scores for Krabby Patty Sales: Help and Examples

[mjhaproff]

Hey everyone!
I am taking a stats class and have a question about a problem I have been assigned. I thought I understood how to calculate a z score, but when posed with this problem, I realized I don't! Here is the question... Can anyone help? I have a z score table and get how that works. I am just not sure which numbers to plug in where...

Spongebob Squarepants lives in a pineapple under the sea, and works at a fast food restaurant called the Krusty Krab. The Krusty Krab wants Spongebob to do a bit of market research on the sales of their best selling item, "The Krabby Patty." Spongebob interviews 1000 of the fish who live in his town, bikini bottom. He determines that on average the residents of Bikini Bottom eat 56 Krabby Patties each year with a standard deviation of 10 Patties. Assume a normal distribution and use Z-scores and the provided Z-Table to compute the following:
What percentage of the sample eats between 30 and 40 Krabby Patties a year?
What percentage of the sample eats between 46 and 66 Krabby Patties a year?
What percentage of the sample eats less than 40 Krabby Patties a year?

 

[I like Serena]

Hey everyone!
I am taking a stats class and have a question about a problem I have been assigned. I thought I understood how to calculate a z score, but when posed with this problem, I realized I don't! Here is the question... Can anyone help? I have a z score table and get how that works. I am just not sure which numbers to plug in where...

Spongebob Squarepants lives in a pineapple under the sea, and works at a fast food restaurant called the Krusty Krab. The Krusty Krab wants Spongebob to do a bit of market research on the sales of their best selling item, "The Krabby Patty." Spongebob interviews 1000 of the fish who live in his town, bikini bottom. He determines that on average the residents of Bikini Bottom eat 56 Krabby Patties each year with a standard deviation of 10 Patties. Assume a normal distribution and use Z-scores and the provided Z-Table to compute the following:
What percentage of the sample eats between 30 and 40 Krabby Patties a year?
What percentage of the sample eats between 46 and 66 Krabby Patties a year?
What percentage of the sample eats less than 40 Krabby Patties a year?

Hi mjhaproff! Welcome to MHB! ;)

The formula for a z-score is:
$$z=\frac{x-\mu}{\sigma}$$
where $x$ is a score, $\mu$ is the mean, and $\sigma$ is the standard deviation.

To find the percentage between 30 and 40 Krabby Patties a year, we need the corresponding z-scores for 30 and 40.
The z score table will tell us the percentage that eats less than 30 Krabby Patties, and also the percentage that eats less than 40 Krabby Patties.
Can we find those z-scores and corresponding probabilities? (Wondering)