Math Answers

1. The management of a grocery store has kept a record of bad checks received per day for a period of 300 days. The data are shown below.

Number of Bad
Checks Received Number of Days
0 12
1 15
2 35
3 55
4 63
5 35
6 38
7 32
8 15

a) Develop a probability distribution for the above data.
b) Is the probability distribution that you found in Part “a” a proper probability distribution? Explain.
c) Determine the cumulative probability distribution, F(x).
d) What is the probability that in a given day the store receives four or less bad checks?
e) What is the probability that in a given day the store receives more than two bad checks?
f) What is the expected value of the number of checks received?
g) Compute the variance of the number of checks received.
h) Compute the standard deviation of number of checks received.

 

The mean value of land and buildings per acre from a sample of farms is ​$1800​, with a standard deviation of ​$300. The data set has a​ bell-shaped distribution. Assume the number of farms in the sample is 78.
​(a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between ​$1200 and ​$2400.

-The position of an object at time t is given by s(t) = -2 - 6t. Find the instantaneous velocity at t = 2 by finding the derivative.

-Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 7 squared as x approaches 7.

The publishers of a business magazine are running a sales promotion for their weekly magazine. The number of prospective customers a sales representative sees per day varies from 1 to 40. The table shows the simulated data of the number of prospective subscribers approached by a sales representative for 8 consecutive weeks.

Day 1 2 3 4 5 6 7
Week 1 20 22 27 17 31 12 39
Week 2 26 13 30 18 24 14 32
Week 3 21 12 22 37 30 23 18
Week 4 15 33 10 28 34 24 22
Week 5 11 33 21 32 26 19 22
Week 6 19 27 20 18 31 14 37
Week 7 29 22 27 30 16 09 36
Week 8 08 28 19 28 25 36 26
If the sales representative is able to get 20% of the prospective customers to subscribe, the maximum expected number of subscriptions per week is . If the sales representative earns $3 per subscription in addition to daily wages, the minimum expected value of the extra income per week is .

Shoe Company orders men’s shoes at a buyer’s meeting in New York City. Because the shoe is designed for spring and summer months, it cannot be expected to sell in the fall. Johnson plans to hold a special August clearance sale in an attempt to sell all shoes not sold by July 31. The shoes cost $40 a pair and retail for $60 a pair. At the sale price of $30 a pair, all surplus shoes can be expected to sell during the August sale. If you were the buyer for the Johnson Shoe Company, how many pairs of the shoe would you order? Assume that the demand for these shoes are normally distributed with a mean of 500 and a standard deviation of 20.

Define a relation R on Z by R={(n,n+3k)| k€Z}.
Check whether R is an equivalence relation or not. If it is, find all the distinct equivalence classes. If R is not an equivalence relation, define an equivalence relation on Z

LaTeX: \left(3\frac{1}{2}-9\frac{3}{4}\right)\div\left(-2.5\right)

A Jar contains 8 green, 4 blue, 10 red, and 2 yellow skittles. A skittle is randomly draw, replaced, then another is drawn. What is the probability of getting a red skittle, then a yellow one?

in the normal destribution 31% of the items are unde 45 and 8% of items are over 64.find the mean and standard deviation of the destribution.

A shoe factory in Umlazi in the district of Durban shows that 30% of customers use a credit card to make payment. On a particular morning, 7 customers purchase shoes from the store. Determine the probability that;
4.2.1 3 customers will pay by credit card. (4 marks)
4.2.2 At least one will pay by credit card. (4 marks)
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4.3 The time it takes a randomly selected job applicant to perform a certain task is normally distributed with a mean value of 120 seconds and a standard deviation of 20 seconds. Determine the probability that a randomly selected candidate will complete the task;
4.3.1 between 100 and 130 seconds. (3 marks)
4.3.2 between 75 and 100 seconds. (3 marks)
4.3.3 within 75 seconds. (2 marks)