Statistics and Probability Answers

a. state the null and alternative hypothesis

b. compute the test statistics

c. determine the critical value and the rejection region

d. draw a conclusion

1. It is claimed that the average weight of babies at birth is 3.4 kg. The average weight of a random sample of 30 newly born babies was determined. It was found out that the average weight was 3.1 kg.

Is there a reason to believe that the average weight of the babies at birth is not 3.4 kg? Assume that the population standard deviation is 1.1 kg. (Use 0.05 level of significance.)

2. Last year, a real estate agent earned an average of ₱40,250.00 a month. Suppose you recently selected a random sample of 25 real estate agents and you have determined how much each of them earns each month. Your computations of their earnings resulted to an average of ₱40,400.00 with a standard deviation of ₱225.00. Using a 0.01 level of significance, can it be concluded that the average monthly earning of real estate agents has increased? Assume normality in the population

one person is to be selected at random from of group of 25 people.the probility that seleact person will ne a male is 0.44 and the probility that selected person will be a male who was born after the 1960 is 0.28 r

According to a study done last year, the average monthly expenses for mobile phone loads of senior high school students in Sta. Rosa was P350.00. A statistics student believes that this amount has increased since January of this year. Is there a reason to believe that this amount has really increased if a random sample of 60 students has an average monthly expenses for mobile phone loads of P380.00? Use a 0.05 level of significance. Assume that the population standard deviation is P77.00.

PROBLEM SOLVING INVOLVING THE NORMAL CURVE CONCEPTS

Given = 30 and = 4.5. Express the raw score for each of the following.

1. z = 1.25

2. z = -1.67

3. z = 2.3

4. z = -0.30

5. z = 1.96

find the corresponding area between z= 0 and each of the following

1. z= 0.85

2. z= 1.27

3. z= 2.86

4. z= -1.05

5. z= -2.96

Use the seven-step method to solve the following.

In a plant nursery, the owner thinks that the lengths of seedlings in a box sprayed with a new kind of fertilizer has an average heights of 26 cm after three days and a standard deviation of 10 cm. One researcher randomly selected 80 such seedlings and calculated the mean height to be 20 cm and the standard deviation was 10 cm. Will you conduct a one-tailed or a two-tailed test? Proceed with the test using = 0.05.

Use the seven-step method to solve the following.

In a plant nursery, the owner thinks that the lengths of seedlings in a box sprayed with a new kind of fertilizer has an average heights of 26 cm after three days and a standard deviation of 10 cm. One researcher randomly selected 80 such seedlings and calculated the mean height to be 20 cm and the standard deviation was 10 cm. Will you conduct a one-tailed or a two-tailed test? Proceed with the test using = 0.05.

A contractor is uncertain of the precise total costs for either materials or labour for a project. In addition, the total line of credit that banks are ready to make available for financing the project is no more than £260,000. Before accepting the project, the contractor wants to know the probability that the total costs will exceed £260,000. It is believed that material costs can be represented by a normally distributed random variable with mean £100,000 and standard deviation £10,000. Labour costs are £1,500 a day and the number of days needed to complete the project can be represented by a normally distributed random variable with mean 80 and standard deviation 12. 

Assuming that material and labour costs are independent, what are the mean and standard deviation of the total project cost (material plus labour costs)? [10 marks] 

b) What is the probability that the total project cost is greater than £260,000? 

1. If three coins are tossed,which is NOT a possible value of the random variable for the number of tails?

A man is at the origin on the x-xis and takes a unit step either to the left or to the right. He stops after 5 steps or if he reaches 3 or -2. How many possible paths the man can travel?