Question

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

Answer 1

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.

Answer 2

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.

`z=(x-\mu)/(\sigma)`, where,

`z` = z-score,

`x` = Random sample score,

`\mu` = Mean,

`\sigma` = Standard deviation.

Upon substituting our given values we will get,

`1.65=(x-3.2)/(0.13)`

`1.65*0.13=(x-3.2)/(0.13)*0.13`

`0.2145=x-3.2`

`0.2145+3.2=x-3.2+3.2`

`3.4145=x`

`x\approx 3.45`

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