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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?
a stone is thrown horizontally from the roof of a building 15 m high with an initial speed of 5 m/s. How long will it take before the ball hits the ground?
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?
Angela’s physician suspects that Angela has just suffered a myocardial infarction, or heart attack. She tells Angela that she is going to take a blood sample so that the hospital lab can perform a test to confirm her diagnosis. What information can Angela’s blood yield to help the physician?
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.
A 50 kg tricycle travelling 6 m/s east and another tricycle with the same mass moving to the west at 3 m/s collided. Suppose the
collision did not damage any of the vehicles but caused the tricycles to move to the west at 3 m/s and to the east at 6 m/s, respectively.
Prove the law of conservation of momentum in this scenario.
#339914 on Dec 2023