Question 1

A food shop buys organic oats in bags of mean weight 1000 grams. It is known that the weights of the bags in any batch are normally distributed with standard deviation 150 grams. A bag of oats is randomly selected, calculate the following probabilities, rounding your final answers to 4 decimal places.

(a) The bag is exactly 750 grams_____

(b) The bag is less than 1225 grams_____

(c) The bag is more than 700 grams_____

(d) The bag is either less than 700 grams or more than 1225 grams______

(e) The bag is between 700 and 1225 grams.______

(f)Bags in the top 5% contains too much oats and must be repackaged. That is the smallest weight a bag could have and still needs to be repackaged?_____grams

Question 2

The weight of gravel, in kilograms, collected by a power shovel may be modeled by a normal distribution with unknown mean, , and standard deviation 50. The weights of a random sample of 20 collections have a mean of 1030 kg.

Answer the following questions round all FINAL answers to two decimal places.

(a) What is the point estimate of the mean weight of gravel that the shovel can collect?_____

(b) Calculate the margin of error for a 99% confidence interval estimate of ______

(c) State the 99% confidence interval for the mean, (_____,___)

d) What sample size is needed so that the error is no more than 15 kg? n =____power shovels

Question 3

Classify the variable as Quantitative (N) and Qualitative (C).

NOTE: If the variable is quantitative enter N

If the variable is qualitative enter C

Number of people in a waiting line_______

Question 4

A coin is tossed four times. Calculate the probability of having all heads. Round your answers to four decimal places._____

For an Economics test the mean score is 100 and the standard deviation is 10, and for an Accounting test the mean score is 50 and the standard deviation is 4. You are given the test scores of a student who took both tests. Determine on which test the student had a better score.

Enter E if the student did better on the Economics test

Enter A if the student did better on the Accounting test

Enter S if the student did relatively the same on both tests.

A student scores 125 on the Economics test and 59 on the Accounting test.

The student did better/same on _____test.

Question 6

8pts

The average cost of a speeding ticket plus court fees is approximately $150. A random sample of 38 speeding ticket court cases showed that the mean cost was $152.59. At the 0.01 level of significance, is that greater than $150? The population standard deviation is $10.78.

STEP 1. State the null and alternate hypothesis

ABCDH0:=150

=

150

H1:<150

<

150

H0:=150

=

150

H1:150

150

H0:=150

=

150

H1:>150

>

150

H0:=150

=

150

H1:=152.59

=

152.59

The hypotheses are_______(Enter an UPPER CASE Letter Only.)

STEP 2. State the critical value(s). Enter the appropriate letter.

ABCDEFGHI=1.28

z = ____

1.28

=1.65

z=

1.65

=2.33

z

=

2.33

=1.28

z

=

1.28

=1.65

z

=

1.65

=2.33

z

=

2.33

=1.65

z

=

1.65

=1.96

z

=

1.96

=2.58

z

=

2.58

z =(Enter a letter only)

STEP 3. Calculate the test value

z =_____(Round to two decimal places)

STEP 4. Make the decision by rejecting or not rejecting the null hypothesis. Since the test value falls in the non-rejection region, we do not reject the null hypothesis.

Conclusion 1. Do not reject the null hypothesis. At the 0.01 significance level, there is not sufficient evidence to conclude that the average cost of speeding tickets plus court fees is approximately $150.

Conclusion 2. Reject the null hypothesis. At the 0.01 significance level, there is sufficient evidence to conclude that the average cost of speeding tickets plus court fees is greater $150.

Conclusion 3. Reject the null hypothesis. At the 0.01 significance level, there is not sufficient evidence to conclude that the average cost of speeding tickets plus court fees is approximately $150.

Conclusion 4. Do not reject the null hypothesis. At the 0.01 significance level, there is sufficient evidence to conclude that the average cost of speeding tickets plus court fees is approximately $150.

______(Enter a number only from the list 1, 2, 3, or 4)