Math Answers

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.

1.use Cramer's rule to solve the equation below (10 marks)

y-z =2

3x+2y+z=4

5x+4y=1

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.

1.4 If Universal Set U = {90, 91 , 92 , 93 , 94, 95 , 96 , 97 , 98, 99 , 100} (10) A = {90, 92, 94, 96, 98, 100}, B= {91, 93, 95, 97, 99}, C = {90, 94, 98}

1.4.1 What is (A ∩ C)c

1.4.2 What is (B ∪ C)c

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

Show that {𝑥} ⊆ ℝ is connected

Show that {𝑥} ⊆ ℝ is connected.