Question

The amount of money that college students spend on food each week during the academic year is normally distributed with
a mean of $31.28 and a standard devitation of $11.42.
What is the probability that one randomly selected student will spend less than $25 per week on food?
If you randomly select 10 students, what is the probability that their mean will be less than 525?

Answer 1

Answer:

~ 70 %

Step-by-step explanation:

(31.28 - 25)/ 11.42    means  25 is .5499  S.D. below the mean

z -score = .7088

 70.88 % chance of less than = 25 dollars

Answer 2

The required probability for one randomly selected student will spend less than $25 per week on food is 0.2911 and for randomly selected 10 students, what is the probability that their mean will be less than $25 is 0.040.

What is probability?

Probability can be defined as the ratio of favorable outcomes to the total number of events.

a) X = 25 , μ = 31.28 and σ = 11.42

$Z = \frac{X - \mu}{\sigma}\\z = \frac{25 - 31.28}{11.42}\\z = -0.5499$

Using z score
Now a probability that one randomly selected student will spend less than $25 per week on food is given.
P(x<25) = p(z = -0.5499)
             = 0.2911

b) number of sample = 10
standard deviation = 11.42/√10
                                = 3.611

Herr,

$Z = \frac{X - \mu}{\sigma}\\z = \frac{25 - 31.28}{3.611}\\z = -1.7444$

Probability (x<25) = p(z = -1.7444)
Using the Z score table,
Probability (x <25) = 0.040

Thus, the required probability for one randomly selected student will spend less than $25 per week on food is 0.2911 and for randomly selected 10 students, what is the probability that their mean will be less than $25 is 0.040.

Learn more about probability here:

brainly.com/question/14290572

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