Question

The accompanying data represent the actual amount (in mL) poured into a short, wide glass for individuals asked to pour 44.3 mL (1.5 ounces).

89.3 68.6 32.7 37.3 39.7 46.7 66.1 79.4 66.4 52.1 47.3
64.4 53.7 63.4 46.2 63.0 92.1 57.6
A) Calculate the values of the mean and standard deviation (in mL).
mean 59.222 mL
standard deviation 16.725 mL
Interpret the values of the mean and standard deviation.
A typical amount poured into a short, wide glass is 19.7 mL. A typical deviation from the mean amount poured is_____mL.
B) The mean amount poured into a tall, slender glass for individuals asked to pour 44.3 mL (1.5 ounces) was 51.283 mL. What do the values of the means for the two types of glasses suggest about the shape of glasses used?
The mean amount for a short, wide glass is greater than the mean amount for a tall, slender glass. This suggests that bartenders tend to pour more into a short, wide glass compared to a tall, slender glass.

Answer 1

Kindly check explanation

Explanation:

Given the data below :

x : 89.3 68.6 32.7 37.3 39.7 46.7 66.1 79.4 66.4 52.1 47.3 64.4 53.7 63.4 46.2 63.0 92.1 57.6

Mean(m) = ΣX / n

ΣX = 1066 ; n = number of observations = 18

Mean(m) = 1066 / 18

Mean = 59.22

Standard deviation (σ) :

Using the online standard deviation calculator :

σ = √(Σ(x - m)²/n-1)

σ = √264.198395

σ = 16.72

The mean amount poured into a glass for the 18 samples is 59.22 while the variation in the data samples from the mean value is 16.72.

typical amount poured into a short, wide glass is 19.7 mL. A typical deviation from the mean amount poured is_____mL.

(59.22 - 19.7) mL = 39.52mL

Mean amount poured into a tall slender glass = 51.283

Mean (short wide glass) = 59.22mL

Mean (tall slender glass) = 51.283mL

Short wide glass > tall slender glass