Question

The acceptable level for insect filth in a certain food item is 4 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 40 ten-gram portions of the food item is obtained and results in a sample mean of x̄ = 4.7 insect fragments per ten-gram portion. Complete parts (a) through (c) below. c) What is the probability a simple random sample of 40 ten-gram portions of the food item results in a mean of at least 4.7 insect fragments? P(x ≥ 4.7) = _____ (Round to four decimal places as needed.)

          The acceptable level for insect filth in a certain food item is 4 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 40 ten-gram portions of the food item is obtained and results in a sample mean of x̄ = 4.7 insect fragments per ten-gram portion. Complete parts (a) through (c) below.

c) What is the probability a simple random sample of 40 ten-gram portions of the food item results in a mean of at least 4.7 insect fragments? P(x ≥ 4.7) = _____ (Round to four decimal places as needed.)

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Added by Derrick R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Joshua Argo

08/23/2022

Step 1

However, it is not given in the problem. Without this information, we cannot calculate the probability. If we had the standard deviation, we would use the Central Limit Theorem to calculate the z-score for 4.7, and then use a z-table to find the probability of Show more…

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The acceptable level for insect filth in a certain food item is 4 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 40 ten-gram portions of the food item is obtained and results in a sample mean of x̄ = 4.7 insect fragments per ten-gram portion. Complete parts (a) through (c) below. c) What is the probability a simple random sample of 40 ten-gram portions of the food item results in a mean of at least 4.7 insect fragments? P(x ≥ 4.7) = _____ (Round to four decimal places as needed.)

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0:00 All right.

00:01 So for this part, we are taking a simple random sample of 40.

00:06 And we know that the acceptable level is four insect fragments for our four insect fragments and per 10 grams.

00:25 And we have a random sample of 40.

00:27 And we get a sample mean of 4 .7, which is more.

00:34 And we're going to see what.

00:35 Is the probability of that.

00:37 Now, the thing that we're missing here is we need to know what is the average number of insect parts and the standard deviation.

00:47 And i'm sure that that is going to be evident within the rest of the problem.

00:51 Let's see if i can find that.

00:55 It's really a gross question, honestly.

01:04 Very nasty term there.

01:07 All right, let's see.

01:08 I'm trying to find that question somewhere.

01:19 So i'm seeing a mean of four and a standard deviation of square root of four.

01:28 Maybe that's what you have.

01:29 If not, you can sub that in, which is two.

01:32 Okay? if not, you can sub that in to what we're about to do.

01:35 So we're looking for the probability of our sample mean being greater than or equal to 4 .7, given this information...

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