Statistics and Probability Answers

Find The following percentiles using this data: 40,45,50,50,56,60,65,80,90

1. 75th percentile

a. 65

b. 56

c. 50

d. 90

2. 95th percentile

a. 65

b. 56

c. 80

d. 90

A coin is tossed C times what is the probability of getting exactly B heads

A shop assistant makes 3 entry errors per week. Find the Probability that in a week chosen at random she will make:

(i) Exactly 2 errors [2 marks]

(ii) At least 2 errors [3 marks]

(b) What is the probability that over a period of two weeks, the shop assistant in part (b) above will commit at least 3 errors?

in a recent survey the average amount of money students have their wallet is 200 with standard deviation of 45. A teacher feels that the average amount is lower . She surveyed 80 randomly selected students and found that the average amount is 35

1 The principal of the school claims that the main age of the teachers is 45 years. The mean age of the randomly selected 35 teachers is 42 years, which is not equal to what is claimed by the principal.

In the class of Statistics, there are 75 students in total out of which 55 male, 20 female students. 10 students need to be selected for the occasion of freshers' reception.

a. What is the probability that 4 of the selected students would be girls?

b. Find out the mean and standard deviation of the binomial distribution.

The amount of time a student taking statistics spends on studying for a test is normally distributed. If the average time spent studying is 10 hours and the standard deviation is 4

hours,

a. What is the probability that a student will spend more than 13 hours studying?

b. What is the probability that a student will spend between 9 to 11 hours studying?

c. What is the probability that a student will spend less than 8 hours studying?

A normally distributed population has a mean of 25.6 and a standard deviation of 3.3. Find the probability that a single randomly selected element X of the population exceeds 30.

The factory owner claimed that their bottled fruit juice has the capacity of less than an average of 280ml. To test the claim, a group of consumers gets a sample of 80 bottles of the fruit juice, calculates the capacity, and then finds the mean capacity to be 265ml. The standard deviation is 8ml. Use a= 0.05 level of significance to test the claim.

Suppose that the lifetimes of electric light bulbs follow an Exponential distribution with mean

1000 hours. A

random sample of 40 light bulbs is tested. The probability that the mean

lifetime is at least 900 hours is: