Elidia100
Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

A company sells cookies in 250-gram packs. When a particular batch of 1,000 packs was weighed, the mean weight per pack was 255 grams and the standard deviation was 2.5 grams. Assuming the data is normally distributed, we can conclude that % of the packs weighed less than 250 grams

Sagot :

apologiabiology
so the deviation was 2.5 grams
that means that the average/mean could have been
255-2.5 or 255+2.5 =   252.5 or 257.5
so if all of them weighed the same, none of them weighed less than 250 so the answer is 0%

Answer:

2.28%

Step-by-step explanation:

We have been given that a particular batch of 1,000 packs was weighed, the mean weight per pack was 255 grams and the standard deviation was 2.5 grams.

We will use z-score formula to solve our given problem.

[tex]z=\frac{x-\mu}{\sigma}[/tex], where,

[tex]z=\text{z-score}[/tex],

[tex]x=\text{Raw score}[/tex],

[tex]\mu=\text{Mean}[/tex],

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

Upon substituting our given values in z-score formula we will get,

[tex]z=\frac{250-255}{2.5}[/tex]

[tex]z=\frac{-5}{2.5}[/tex]

[tex]z=-2[/tex]

Now we will use normal distribution table to find the area corresponding to z-score of -2.

Using normal distribution table we will get,

[tex]P(z<-2)=0.02275[/tex]

To convert our answer to percentage we will multiply 0.02275 by 100.

[tex]\text{Percentage of packs weighed less than 250 grams}=0.02275\times 100[/tex]

[tex]\text{Percentage of packs weighed less than 250 grams}=2.275\%\approx 2.28\%[/tex]

Therefore, 2.28% of the packs weighed less than 250 grams.

Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.