The weight of a small Starbucks coffee is a random variable with a mean of 360 g and a standard
deviation of 9 g. Use Excel to find the weight corresponding to each percentile of weight.
a. 10th percentile b. 32nd percentile c. 75th percentile
d. 90th percentile e. 99.9th percentile f. 99.99th percentile
I don't know how you are using Excel, except if it has the proportions of a normal distribution.
Z = (score-mean)/SD = (score-360)/9
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the Z scores that correspond to the above proportions. Insert the Z scores in the equation above to find the scores(weights).
To find the weight corresponding to each percentile of weight, we need to use the standard normal distribution in Excel. The standard normal distribution is a probability distribution that has a mean of 0 and a standard deviation of 1.
To find the weight corresponding to a specific percentile, we can use the NORM.INV function in Excel. This function takes the percentile value and returns the corresponding value from a normal distribution.
In this case, we need to adjust the percentiles to match the mean and standard deviation of the Starbucks coffee weights. We can do this by using the formula: value = mean + (percentile * standard deviation).
Let's calculate the weight corresponding to each percentile:
a. 10th percentile:
value = mean + (percentile * standard deviation)
value = 360 + (0.1 * 9)
value = 360 + 0.9
value = 360.9 grams
b. 32nd percentile:
value = mean + (percentile * standard deviation)
value = 360 + (0.32 * 9)
value = 360 + 2.88
value = 362.88 grams
c. 75th percentile:
value = mean + (percentile * standard deviation)
value = 360 + (0.75 * 9)
value = 360 + 6.75
value = 366.75 grams
d. 90th percentile:
value = mean + (percentile * standard deviation)
value = 360 + (0.9 * 9)
value = 360 + 8.1
value = 368.1 grams
e. 99.9th percentile:
value = mean + (percentile * standard deviation)
value = 360 + (0.999 * 9)
value = 360 + 8.991
value = 368.991 grams
f. 99.99th percentile:
value = mean + (percentile * standard deviation)
value = 360 + (0.9999 * 9)
value = 360 + 8.9991
value = 368.9991 grams
So, the weights corresponding to each percentile are:
a. 10th percentile: 360.9 grams
b. 32nd percentile: 362.88 grams
c. 75th percentile: 366.75 grams
d. 90th percentile: 368.1 grams
e. 99.9th percentile: 368.991 grams
f. 99.99th percentile: 368.9991 grams