Respuesta :
Answer:
32.64% probability that you would have enough money to pay for all five baskets of fries
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sample means with size n can be approximated to a normal distribution with mean
In this problem, we have that:
[tex]\mu = 6, \sigma = 2, n = 5, s = \frac{2}{\sqrt{5}} = 0.8944[/tex]
You want to get 5 baskets of fries but you only have $28 in your pocket. What is the probability that you would have enough money to pay for all five baskets of fries?
28/5 = 5.6
So this is the pvalue of Z when X = 5.6.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5.6 - 6}{0.8944}[/tex]
[tex]Z = -0.45[/tex]
[tex]Z = -0.45[/tex] has a pvalue of 0.3264
32.64% probability that you would have enough money to pay for all five baskets of fries
