Question

The bottle of Maria’s favorite sports drink says that it holds 20 fluid ounces. Maria suspects that the sports drink actually holds a different amount. Maria takes a random sample of 25 bottles and measures the number of fluid ounces in each bottle. The mean fluid ounces of Maria’s sample of 35 sports drinks is 21.5 fluid ounces. Assume that the standard deviation of fluid ounces for the entire population of sports drinks is 2 fluid ounces. True or false? Finding a random sample with a mean this high in a population with mean 20 fluid ounces and standard deviation 2 fluid ounces is very unlikely. Group of answer choices True False

Answer 1

Answer: False.

Step-by-step explanation: Standard Deviation (Dp) is how spread the number is. If a value is closer to the mean, its standard deviation is low. On the other hand, if standard deviation is higher, the value is spread out over a wider range.

Formula to calculate:

Dp = √∑(x - μ)² / n

where: μ is the mean and n is sample size

Dp = $\sqrt{\frac{(21.5-20)^{2} }{25} }$

Dp = $\sqrt{\frac{1.5^{2} }{25} }$

Dp = $\frac{1.5}{5}$

Dp = 0.3

The standard deviation of Maria's little experiment is 0.3 and not 2, so the sentence is false.