# Probability and Statistics - Practice Tests and Solutions

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Try Udemy for Business- This Practice Tests course is designed to refresh your understanding of topics related to probability and statistics.
- Test your knowledge on topics related to probability and statistics before taking the ASQ CQE, CSSGB or the CSSBB exam.

- A simple calculator with statistical functions - eg TI-30Xa

*Learn probability and statistics by solving problems.*

This course will test your understanding of the basic concepts related to Probability, Statistics and Data Analysis. More than 100 questions with solutions have been included in this course.

Following areas of statistics are covered:

**Descriptive Statistics **- Mean, Mode, Median, Quartile, Range, Inter Quartile Range, Standard Deviation

**Data Visualization** - Commonly used charts such as Histogram and Box and Whisker Plot

**Probability** - Basic Concepts, Permutations, Combinations

**Probability Distributions** - Normal, Binomial and Poisson Distributions

**Hypothesis Testing **- One Sample and Two Samples - z Test, t-Test, p Test, F Test, Chi-Square Test

**ANOVA -** Analysis of Variance (ANOVA)

- Quality professionals appearing in the ASQ exams (such as CQE, CSSGB, CSSBB)

Download the file under resources for probability distributions tables.

The probability that a random person has lung cancer is 0.0025 and the probability that the person has lung cancer and is also a heavy smoker is 0.002. Given that someone picked at random has lung cancer, what is the probability that the person is a heavy smoker?

A test for a rare disease is 99 percent correct most of the time (meaning if you have the disease, it will show that you do with a 99 percent probability, and if you do not have this disease, it will show that you don’t with a 99 percent probability).

The disease is very rare, and it occurs randomly in the population in one per 10,000 people.

If you get back the test results as positive, calculate the probability that you have the disease?

On a booking counter on the average 3.6 people come every 10 minute on weekends. You have been asked by your manager to find out the probability of getting more than 7 people in 10 minutes. What probability distribution would you use to solve this problem?

The mean weight of 1000 students at a certain college is 62 Kg and the standard deviation is 5Kg. Assuming that the weights are normally distributed, find the probability that a randomly selected student weighs between 55 and 60 Kg?

A battery manufacturer claims that the battery lasts for 300 hours. An independent tester checks 15 batteries and find out the average life to be 280 hours with the standard deviation of 24 hours. What is the t-statistic in this example?

Bolts produced by a machine have a mean weight of 50 gm and a standard deviation of 2 gm. If 300 random samples of size 36 are drawn from this population, determine the expected mean and standard deviation of the sampling distribution of means.

One thousand bolts produced by a machine have a mean weight of 50 gm and a standard deviation of 2 gm. What is the probability that a random sample of 100 bolts selected from this group will have a combined weight greater than 5,200 gm?

Researchers want to determine the sleeping time each night in India. A study of a random sample of 100 Indians found the average amount of time people sleep each night is 6.3 hours with a standard deviation of 2.6 hours. Use the sample of data to construct a 95% confidence interval to estimate the true mean amount of time people in India sleep each night.

A teacher found that in a sample of 80 students, 17 said they use social media while doing their homework. Use the sample of data to construct a 90% confidence interval to estimate the true proportion of students using social media while doing their homework.

A medicine has a 66% success rate. The composition of the medicine was modified to improve its effectiveness. We want to test if with the new composition more than 66% get cured.

Which of the following is the correct null and alternate Hypothesis?

A lubricating oil manufacturing company continually monitors the viscosity of the oil. If the viscosity from sample data drops below a specified level, the production process is halted, and the machine is readjusted. Which of the following would result from a Type I error?

The average breaking strength of steel rods is required to be at least 35,000 psi. Based on the historical information the standard deviation of breaking strength is 1,500 psi. A random sample of four specimens had the strength as piece one 32,000, piece two 36,000, piece three 34,000 and piece four 34,500.

Which of the following hypothesis tests would you conduct?

The average breaking strength of steel rods is required to be at least 35,000 psi. Based on the historical information the standard deviation of breaking strength is 1,500 psi. A random sample of four specimens had the strengths as: piece one 32,000, piece two 36,000, piece three 34,000 and piece four 34,500.

What will be null and alternate hypothesis is this case?

The average breaking strength of steel rods is required to be at least 35,000 psi. Based on the historical information the standard deviation of breaking strength is 1,500 psi. A random sample of four specimens had the strengths as: piece one 32,000, piece two 36,000, piece three 34,000 and piece four 34,500.

Calculate the test statistic.

The average breaking strength of steel rods is required to be at least 35,000 psi. Based on the historical information the standard deviation of breaking strength is 1,500 psi. A random sample of four specimens had the strengths as: piece one 32,000, piece two 36,000, piece three 34,000 and piece four 34,500.

What would you conclude from this test with a 95% confidence level?

A random sample of 15 batteries resulted in the average life of 280 hours with a standard deviation of 24 hours. Assume the battery life to be normally distributed and α = 0.05 test the following hypothesis:

Ho: ? = 300 hours| Ha: ? ≠ 300 hours

A survey claimed that 23% of adults in the country read a printed newspaper. A city newspaper does not agree with it and assumes that the percentage is more than 23% in the city. A city-wide survey was conducted. Out of 500 adults surveyed 124 people confirmed that they read the printed newspaper. Using the level of significance of 0.05 what would you conclude from this information?

Conduct the following hypothesis using the given data. What would you conclude?

From vendor A we test 200 pieces and find 30 defectives. From vendor B we test 100 pieces and we find 13 defectives. Conduct the two proportions test, to check if there is a significant difference in the quality of these two vendors. Use the Confidence level as 95%.

Two random samples taken from two normal populations yielded the following information. An F Test was conducted with a 95% confidence level to check if the second sample has a higher variation. What will be the critical value of F?

A fair coin is flipped 100 times, and the numbers of heads are counted. This experiment was repeated five times, and the resulted number of heads were: 51, 56, 54, 60 and 50. Is the coin biased? Check with a 95% confidence level.

To test the effectiveness of a medicine, 235 patients were administered this medicine. The below table provides the gender vs effectiveness contingency table. What is the probability that it has a negative impact on a male?

*To test the effectiveness of a medicine, 235 patients were administered this medicine. The below table provides the *gender vs effectiveness contingency table. Is the drug effectiveness dependent upon gender? Test with a 95% confidence level.