Statistics and Probability Answers

On a recent mathematics test, the mean score was 75 and the standard deviation was 5.
Jhon got 93. Would his mark be considered an outlier if the marks were normally distributed? Explain your answer ?

Supermarket CRM system has past records;
a supermarket finds that 26% of people who enter the supermarket will make a purchase. 18 people enter the supermarket during a one-hour period.
(a) What is the probability that exactly 10 customers, 18 customers and 3 customers make a purchase?
(b) Find the expected number of customers who make a purchase.
(c) Find the variance and standard deviation of the number of customers who make a purchase.

Computing Research team doing survey of raining in America.
City of London typically has rain on about 16% of days in April.
(a) What is the probability that it will rain on exactly 5 days in April? 15 days?
(b) What is the mean number of days with rain in April?
(c) What is the variance and standard deviation of the number of days with rain in April?
(d) How probability theories relate to Artificial intelligent programming?

A discrete random variable X has the following probability distribution:

x - 1, 2, 3, 4
P(X=x) - 1/3, 1/3, k, 1/4

Where k is a constant.
(a) Find the value of k.
(b) Find P(X ≤3).

John and Sarah play a game using two 10p coins. The coins are tossed and John records her score using the random variable S and Sarah uses the random variable T.
After a large number of tosses they compare their scores.
Comment on any likely differences or similarities. Please describe your answer?

A bag contains 6 Pink balls, 5 yellow balls and 4 red balls. Three are selected at random without replacement.
Find the probability that
(a) they are all pink
(b) two are blue and one is yellow
(c) there is one of each color .
(d) Brief your answers accordant to theories

A bag contains 14 identical balls, 4 of which are red, 5 black and 5 white. Six balls are drawn from the bag. find the probability that
(i) 3 are red, (ii) at least two are white.

In a certain group of 15 students, 5 have graphics calculators and 3 have a Laptop at home (one student has
both). Two of the students drive themselves to campus each day and neither of them has a graphics calculator nor
a Laptop at home. A student is selected at random from the group.
((a) Find the probability that the student either drives to campus or has a graphics calculator.
(b) Show that the events “the student has a graphics calculator” and “the student has a Laptop at home” are
independent.
Let G represent the event “the student has a graphics calculator”
H represent the event “the student has a Laptop at home”
D represent the event “the student drives to campus each day”
Represent the information in this question by a Venn diagram. Use the above Venn diagram to answer the questions.

A certain “Covid 19” disease occurs in 1% of the population. A simple screening procedure is
Available and in 8 out of 10 cases where the patient has the disease, it produces a positive result. If
The patient does not have the disease there is still a 0.05 chance that the test will give a positive result.
Find the probability that a randomly selected individual:
(a) Does not have the “Covid 19” disease but gives a positive result in the screening test
(b) Gives a positive result on the test
(c) Ton has taken the test and her result is positive. Find the probability that he has the
“Covid 19” disease.
Let C represent the event “the patient has the disease” and S represent the event “the screening test gives a
positive result”. ”.