The average weight of a medium size egg is found to be 3.2 oz, with a standard deviation of 0.13 oz. What is the heaviest egg (to 2 decimal places) that we are 95% confident is still medium size? 3.2 oz 3.33 oz 3.45 oz 3.46 oz

3.2 + 2(0.13) = 3.46
95% of medium sized eggs lie within 2 standard deviations of the mean either side.
So, you just have to add 2 standard deviations to the mean; this will give the greatest possible weight you can expect 95% of medium sized eggs to have.

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ApusApus ApusApus · Answer 2 · 2019-01-23T08:46:32+01:00

Answer:

C. 3.45 oz.

Step-by-step explanation:

We have been given that average weight of a medium size egg is found to be 3.2 oz with a standard deviation of 0.13 oz.

Let us find z-score corresponding to 95% of the data under normal distribution curve. Using normal distribution table we get that 95% of area under the normal curve corresponds to z-score of 1.65.

Now we will use z-score formula to find our sample score.

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

[tex]z[/tex] = z-score,

[tex]x[/tex] = Random sample score,

[tex]\mu[/tex] = Mean,

[tex]\sigma[/tex] = Standard deviation.

Upon substituting our given values we will get,

[tex]1.65=\frac{x-3.2}{0.13}[/tex]

[tex]1.65*0.13=\frac{x-3.2}{0.13}*0.13[/tex]

[tex]0.2145=x-3.2[/tex]

[tex]0.2145+3.2=x-3.2+3.2[/tex]

[tex]3.4145=x[/tex]

[tex]x\approx 3.45[/tex]

Therefore, the greatest weight of a medium size egg is 3.45 oz and option C is the correct choice.