Statistics and Probability Answers

An elevator starts with 4 passengers and stops at 4 floors. Find the probability of the following events:

1) all passengers leave at the same floor (Event A)

2) all passengers leave at the two floors (Event B)

3) all passengers leave at the three floors (Event C)

4) all passengers leave at different floors (Event D)

A Biotech company produces enzymes at a rate that can be described by the Poisson process.

Their lipase enzyme from a genetically modified bacteria produces glycerol at an average rate of

3 mg/L per minute.

4.1 Find the probability that the enzyme will produce exactly 5 mg/L in a given minute. (2)

4.2 What is the likelihood that the enzyme will produce four or more mg/L in a given minute? (7)

4.3 What chance is there that no product will be produced in a given minute?

The manager of a local gym has determined that the length of time patrons spend at the gym is a

normally distributed variable with a mean of 80 minutes and a standard deviation of 20 minutes.

5.1 What proportion of patrons spends more than 2 hours at the gym? (3)

5.2 What proportion of patrons spend less than 1 hour at the gym? (3)

5.3 What is the least amount of time spent by 60% of patrons at the gym?

Calculate the average price paid per kilogram of sodium hydroxide in a lab storeroom consisting

of 40 kilograms bought for R15 each; 10 kilograms bought for R20 each; 5 kilograms bought for

R40 each; and 50 kilograms bought for R10 each.

The heights of male are normally distributed with mean of 170 cm and standard deviation of 7.5cm. Find the probability that a randomly selected male has a height > 180 cm.

Customers arrive at a shopping mart randomly at a rate of 7 per hour.

a)     Find the probability that during any 90 minutes’ period, the number of customers arriving at the shopping mart is exactly 8.

b)     If a customer arrives at 11.30 am, find the probability that the next patient arrives before 11.45 am.

The average on a history exam was 85 out of 100 points, with a standard deviation of 15. Was the distribution of the scores on this exam symmetric? If not, what shape would you expect this distribution to have? Explain your reasoning.

At a restaurant 80% of the users pay using credit cards. Find the probability that in a randomly selected sample of 5 users, exactly 2 users pay using credit cards.

3. What is the 99.5th percentile in a t-distribution with 9 degrees of freedom?

a. 2.764 b. 3.250 c. 3.169 d. 2.821

4. To estimate the mean price of e-books of senior high schools, with a standard deviation of P80, how many e-books are needed to be selected as samples if we wanted to be 95% confident that the sample mean of e-books is within P20 of the true population?

a. 59. b. 60 c. 61 d. 62

5. Which of the following is the appropriate sample size given a standard deviation of 6.4, confidence interval of u 98% and a margin of error or maximum allowable deviation of 2.35?

a. 39 b. 40 c. 41 d. 42

1. t - distribution is a probability distribution used to estimate parameters EXCEPT

when :

a.. the population standard deviation is known

b. the sample size is small.

d. the sample size is small and population variance is unknown

2. t distribution is also known as:

c. the population variance is unknown

a. Teacher's t distribution b. z-distribution

c. Student's t - distribution d. Teacher's z - distribution