Respuesta :
Answer:
C. 0.50
Step-by-step explanation:
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Let X the random variable who represent the weight for bags of chips of a population, and for this case we know the distribution for X is given by:
n=16 represent the sample size
[tex]\mu =16[/tex] represent the true mean
[tex]\sigma=1.5[/tex] represent the population standard deviation
[tex]X \sim N(16,1.5)[/tex]
Where [tex]\mu=16[/tex] and [tex]\sigma=1.5[/tex]
And let [tex]\bar X[/tex] represent the sample mean, the distribution for the sample mean is given by:
[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]
The probability that the sample mean weight is below 16 oz is:
[tex]P(\bar x<16)=P(Z<\frac{16-16}{\frac{1.5}{\sqrt{36}}})=P(Z<0)=0.5[/tex]
So the best option for this case is 0.5
