Statistics and Probability Answers

1. The blood groups of 200 people are distributed as follows: 40 have type A blood, 75 have type B blood, 60 have type O blood, and 25 have type AB blood. If a person from any of the group is selected at random, what is the probability that this person has an O blood type? How about the AB blood type?

1. The weight of goats at a farm is normally distributed with a mean of 60 kg and a standard deviation of 10 kg. A truck used to transport goats can only accommodate not more than 650 kg. If 10 goats are selected at random from the population, what is the probability that the total weight exceeds the maximum weight?

According to a factory employer, the mean working time of workers in the factory is 6 hours with a standard

deviation of 0.5 hours. A researcher interviewed 50% of the employees and found out that their mean working

time is 8 hours with a standard deviation of 1 hour. The 𝛼 level is 0.05.

Instruction: Use the seven-step method to solve the following.

In a vegetables nursery, the caretaker thinks that the lengths

of seedlings in a box sprayed with a new kind of fertilization

has an average height of 16cm after three days and a

standard deviation of 5cm. One researcher randomly selected

60 such seedlings and calculated the mean height to be 12cm

and standard deviation was 5cm. Will you conduct a onetailed test or two tailed test. Proceed with the test using

α=0.05..

The scores for a mathematics course seem to be normally distributed with mean 70 & standard deviation of 8. If the instructor wishes to give an A grade to 10% of the students, what should be the dividing line between an A grade and a B grade?

The scores for a mathematics course seem to be normally distributed with mean 70 & standard deviation of 8. If the instructor wishes to give an A grade to 10% of the students, what should be the dividing line between an A grade and a B grade?

The random variable Y = LogX has N(12,6) distribution. Find (a) The pdf of X (b) Mean and variance of X (c) P ( X ≤ 1000

The random variable Y = LogX has N(10,4) distribution. Find (a) The pdf of X (b) Mean and variance of X (c) P ( X ≤ 1000

n a farming community, 30% of the farmers grow oranges only, 10% grow lemons only and 4% grow both oranges and lemons. 1.1) What proportion of farmers in the community grow either oranges or lemons? [3 marks] 1.2) If a farmer is chosen randomly from these in the community, what is the probability that he grows neither oranges nor lemons? [marks] 1.3) Of all the farmers who grow oranges, what proportion grow lemons also?

What proportion of farmers in the community grow either oranges or lemons