Statistics and Probability Answers

Answer the question below

In a math test, the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probability that the score will lie: 

If the score is above 58

If the score is below 49

If the score is below 68

If the score is above 55

If the score is above 38

you have a 90% chance of passing this IE 223 course if you get 

an 85 or higher on your midterm test. However, if you think you only have a 50% 

chance of scoring an 85 or higher in taking the test. Calculate the chances that 

both of your scores are 85 or higher.

According to the World Health Organization’s statistics published in 2018, the lifespan of a person 

in the Philippines is 67 years old. A random sample of 25 obituary notices in the Philippine Daily 

Inquirer has an average mean of 60 years old with a standard deviation of 19 years. If the life 

span in the Philippines is normally distributed, does this information indicate that the population 

mean life span of Filipinos is less than 67 years old? Use 5% level of significance.

Find the area under the normal curve in each of the following cases. First Draw the normal curve then label it.

1. to the right of𝑧 = 1.63

2. between 𝑧 = −1.36 and 𝑧 = 2.55

3. to the left of𝑧 = −1.78

4. between 𝑧 = −2.76 and 𝑧 = −1.25

5. between 𝑧 = 1.56 and 𝑧 = 2.51

For nos. 9-10, refer to the problem below:

Choc-o is sold in packets with an advertised mean weight of 0.5kgs. The standard deviation is known to

be 0.11 kilograms. A consumer group wishes to check the accuracy of the advertised mean and takes a

sample of 36 packets finding an average weight of 0.47kgs.

______ 9. What test statistic should be used?

A. population mean B. t-test C. z-test D. standard deviation

______ 10. What is the computed value?

A. – 1. 636 B. -1.488 C. 0. 833 D. 5. 551

The Corona!

Directions: Determine the test statistic to be used, then find its computed

vale.

The Coronavirus Disease (COVID-19) is an infectious disease caused

by a new strain of coronavirus. The World Health Organization (WHO) claims

that the incubation period of the virus in the infected person has a mean of

5.1 days. The doctors in the Philippines conducted a research and they

found out that incubation period of the virus in human body is 6.03 days

with a standard deviation of 3.32. The samples were 46 COVID patients. Is

there enough evidence to conclude that the incubation period of the virus is

5.1 days as stated, at α = 0. 01?

Find the 99th percentile of the normal curve

Determine the number of possible outcomes in tossing 2 dies choices:

20 25 36 45

Consider a population with values (2,5,7,8)

a. Find the population mean.

b. Find the population variance.

c. Find the population standard deviation.

d. Find the possible samples of size 2 that can be drawn with replacement from this population.

Suppose the scores of students on a test are normally distributed with a mean score of 70 points and a standard deviation of 10 points. It is decided to give A’s to 10 percent of the students and B’s to 23 percent of the students. Find what scores should be assigned A’s and B’s.