Question

1. The amount of meat on a Subbies foot-long sub follows a Normal distribution, with a mean of 8 ounces and a standard deviation of 0.6 ounce. A random sample of 25 subs is selected every day and measured. What is the probability that the mean weight will exceed 8.2 ounces?

0.0478 0.9521 0.3333 0.6667 0.12

2.

Micah is cooking a pork roast for his family. He wants to be sure the pork roast has an internal temperature of at least 145 degrees Fahrenheit. He uses a thermometer to measure the internal temperature at three randomly chosen places. The minimum reading in the sample is 152 degrees Fahrenheit. Identify the population, the parameter, the sample, and the statistic.

Population, minimum temperature of 145 degrees Fahrenheit; parameter, all pork meat; sample, three random thermometer readings; statistic, minimum sample reading of 152 degrees Fahrenheit Population, all pork meat; parameter, minimum temperature of 145 degrees Fahrenheit; sample, three random thermometer readings; statistic, minimum sample reading of 152 degrees Fahrenheit Population, all pork meat; parameter, minimum temperature of 145 degrees Fahrenheit; sample, minimum sample reading of 152 degrees Fahrenheit; statistic, three random thermometer readings Population, three random thermometer readings; parameter, all pork meat; sample, minimum temperature of 145 degrees Fahrenheit; statistic, minimum sample reading of 152 degrees Fahrenheit Population, minimum sample reading of 152 degrees Fahrenheit; parameter, all pork meat; sample, minimum temperature of 145 degrees Fahrenheit; statistic, three random thermometer readings

3.

Fifty-eight percent of the fish in a large pond are minnows. Imagine scooping out a simple random sample of 20 fish from the pond and observing the sample proportion of minnows. What is the standard deviation of the sampling distribution? Determine whether the 10% condition is met.

The standard deviation is 0.1104. The 10% condition is not met because there are less than 200 minnows in the pond.  The standard deviation is 0.1104. The 10% condition is met because it is very likely there are more than 200 minnows in the pond.  The standard deviation is 0.8896. The 10% condition is met because it is very likely there are more than 200 minnows in the pond.  The standard deviation is 0.8896. The 10% condition is not met because there are less than 200 minnows in the pond.  We cannot determine the standard deviation because we do not know the sample mean. The 10% condition is met because it is very likely there are more than 200 minnows in the pond.

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Answer #1

Solution:

Question 1)

Given: The amount of meat on a Subbies foot-long sub follows a Normal distribution, with a mean of 8 ounces and a standard deviation of 0.6 ounce.

That is:

Sample size = n = 25

We have to find: the probability that the mean weight will exceed 8.2 ounces.

That is:

Find z score:

Thus we get:

Now look in z table for z = 1.6 and 0.07 and find area.

P( Z < 1.67) =0.9525

Thus

Closest answer from choices is: 0.0478

thus correct answer is: 0.0478

To get exact answer we need to use Excel command and z value rounded to at least 4 decimal places as 1.6667

=1-NORM.S.DIST( z , cumulative)

=1-NORM.S.DIST( 1.6667 , TRUE)

=0.0478

Thus the probability that the mean weight will exceed 8.2 ounces = 0.0478

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