Statistics and Probability Answers

Through careful record keeping, you have the times to burn out of 100 Bright brand light bulbs. The average time to burn out is 200 hours, with a standard deviation of 12 hours. Give a 95% confidence interval for the mean time to burn out of this brand of light bulb.

If the systolic pressure for a certain group of obese people has mean of 132 and a standard deviation of 8, find the probability that a randomly selected person will have the following blood pressure. Assume the variable is normally distributed.

a. Above 130

b. Below 150

c. Between 125 - 158

The leader of the jeepney drivers’ association claims that the average daily take-home pay of all jeepney drivers in Pasay city is Php 400.00. A random sample of 100 jeepney drivers in Pasay city was interviewed and the average daily take-home pay of these drivers is found to be Php 425. Use a 0.05 level of significance and assume the standard deviation is Php 92.

 Ծ = 92          Ẋ = 425           ﬠ = 400           n = 100         level of significance = 0.05

1. State the hypothesis

  Ho: u = 400

  Ha: u ‡ 400

2. Type of test: Two-tailed test

3. Critical Value

4. Test statistics

5. Reject or accept the null hypothesis

2. Assume that the weights of a teenager were normally distributed with the mean of 63 kg. and a standard deviation of 2.5 kg.

a. What is the probability that their mean weight is greater than 62 kg?

b. If 70 teenagers are randomly selected, what is the probability that the mean weight is greater than 62 kg?

1. The height of the students in Bataan National High School- SHS has a mean of 151 cm with the standard deviation of 6. Assume that the variable is normally distributed.

a. What is the probability that their mean height is less than 150 cm?

b. If 50 of them are taken as samples, what is the probability that their mean height is less than 150cm?

1. A population consists of the values (2, 4, 7). List down all the possible samples of size 2 which can be drawn with replacement from this population.

Sketch and Shade. Given the following critical values and blank normal curve, draw the line then shade

Level of Signifinance

90 %

Critical value

t = -1.282

Level of Signifinance

99%

Critical Value

z= ± 2.56

Level of Signifinance

95%

Critical Value

z= 1.65

The mean height of random sample of 100 individuals from a population is 160 cms. The

S.D. of the sample is 10cms. Would it be reasonable to suppose that the mean height of the

population is 165cms?

Table Completion. Supply the missing part of the table using the problem stated below.

“A random sample of 200 business managers were administered a develop Managerial Skills Test.

The sample mean and the standard deviation were 78 and 4.2, respectively. In the standardization of the

test, the mean was 73 and the standard deviation was 8. Test for significant difference using 𝛼 = 0.05

utilizing the p- value method.”

Table Completion. Supply the missing part of the table using the problem stated below.

“A random sample of 200 business managers were administered a develop Managerial Skills Test.

The sample mean and the standard deviation were 78 and 4.2, respectively. In the standardization of the

test, the mean was 73 and the standard deviation was 8. Test for significant difference using 𝛼 = 0.05

utilizing the p- value method.”