One Touch Ent. Sells mobile phones as well as other communication gadgets. TABLE 2 shows the probability distribution for the number of mobile phones sold per d

Question

TABLE 2

No.of mobile phones sold: 15 16 17 18 19 20 per day, X

P(X = x): 0. 12 0.15 0.20 0.25 0.17 0.11

i. Show that the above distribution is a probability distribution of the random variable Χ.
ii. Is it possible for the store to sell more than 20 mobile phones per day? Justify your answer.
iii. Calculate the expected number of mobile phones sold per day at the store. Interpret
the results.
iv. Compute the standard deviation of the number of mobile phones sold per day at the Store
Question 2: a) According to the social Survey conducted at New York city, 45% of employed adults believed that if they lost their job, it would be easy to find another with a similar salary. Suppose that TEN (10) employed adults are randomly selected.

i. What is the probability distribution for the above problem?

ii. Find the probability that more than TWO (2) of them believe it would be easy to find another job.

iii. Is it unusual that all of them believe it would be easy to find another job? Explain your answer.

b) The number of messages received by a computer bulletin board follows a Poisson distribution with a mean of EIGHT (8) messages per hour.

i. What is the probability that FIVE (5) messages are received in an hour?

ii. What is the probability that less than THREE (3) messages are received in half an hour?

c) The Vehicle Speeds at a certain location in PLUS highway can be described by a normal distribution. The mean speed is 110 km/h, and the standard deviation is 10 km/h. Find the percentage of vehicle speeds at this location which are faster than 123 km/h.

QUESTION 3: a) A student has an evening job as a waiter in a restaurant, for which the monthly incomes are normally distributed with a mean of $ 400 and a standard deviation of $ 80.

i. Without doing any calculations, what is the median that the student can earn in a month? Explain your answer.

ii. What is the probability that the student will earn between $ 480 and $ 560 in a month?

iii. At most, how much will the student earn in 90% of the time?

iv. In a sample of 4 months, on average what is the chance that the student earns between $ 480 and $560 per month?

v. Compare your answers in part (ii) and part (iv). Is there any differences and why?

b) A certain delivery truck can safely carry a load of 1542 kilograms. The cartons that will be loaded onto the truck have a mean weight of 36 kilograms with a standard deviation of 9 kilograms. 40 cartons are loaded onto the truck.

i. If the total weight of the 40 cartons is 1542 kilograms, what is the sample mean weight?

ii. What is the probability that the truck can deliver the 40 cartons safely?

iii. Give comment based on answer in part (iii).

Answer 1

i. add all the probabilities to show it is equal to 1

ii. Any number outside the distribution shown above has a probability of zero, meaning it is impossible

iii. calculate the expected value by multiplying each X times its P(X)  (example 15(.12)...)  and then add your 6 products.

 

µ=E(X)=∑Xp(X)

 

iv. once answer in iii is found, subtract each X from the distribution from this value square the difference and multiply by the corresponding probability.

 

∑(X-µ)²p(X)

 

do this for each X and then add your 6 numbers

 

take a square root of your sum and there ya go

If that doesn't make sense, recommend setting up a lesson so you can see it on a whiteboard.
You probably should only ask one question at a time.