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An automatic filling machine in a factory fills bottles of ketchup with a mean of 17.6 oz and a standard deviation of 0.05 oz with a distribution that can be well modeled by a Normal model. What is the probability that a bottle of ketchup contains less than 17.5 ​oz?

Respuesta :

JeanaShupp

Answer: 0.0228

Step-by-step explanation:

Given : [tex]\text{Mean}=\mu=17.6\ oz[/tex]

[tex]\text{Standard deviation}=\sigma=0.05\ oz[/tex]

Since , the distribution follows a Normal distribution .

The formula to calculate the z-score is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x=17.5 oz

[tex]z=\dfrac{17.5-17.6}{0.05}=-2[/tex]

The p-value = [tex]P(z<-2)=0.0227501\approx0.0228[/tex]

Hence, the required probability : 0.0228

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