Probability Distributions

Question 10:(a) It is found that 60% of the students from a certain class obtained grade A in English in O level trial examination.If 10 students from the class are selected at random, find the probability that(i) exactly 7 students obtained grade A.(ii) not more than 7 students obtained grade A.(b) Diagram below shows a … Read more

Question 8:(a) A survey is carried out about red crescents in a school.It is found that the mean of the number of red crescents is 315, the variance is 126 and the probability that a student participate in red crescents is p.(i) Find the value of p.(ii) If 8 students from the school are chosen … Read more

Question 5: The diameter of oranges harvested from a fruit orchard has a normal distribution with a mean of 3.2 cm and a variance of 2.25 cm. Calculate (a) the probability that an orange chosen at random from this fruit orchard has a diameter of more than 3.8 cm. (b) the value of k if 30.5 % … Read more

Question 1: In a school examination, 2 students out of 5 students failed Chemistry. (a)    If 6 students are chosen at random, find the probability that not more than 2 students failed Chemistry. (b)   If there are 200 Form 4 students in that school, find the mean and standard deviation of the number of students … Read more

Question 3: The masses of mangoes in a stall have a normal distribution with a mean of 200 g and a standard deviation of 30 g. (a) Find the mass, in g, of a mango whose z-score is 0.5. (b) If a mango is chosen at random, find the probability that the mango has a … Read more

Question 1: Diagram below shows the graph of a binomial distribution of X. (a) the value of h, (b) P (X ≥ 3) Solution: (a) P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4) = 1 1 16 + 1 … Read more

5.2c Probability of an Event Example: The masses of pears in a fruit stall are normally distributed with a mean of 220 g and a variance of 100 g. Find the probability that a pear that is picked at random has a mass (a) of more than 230 g. (b) between 210 g and 225 … Read more

5.2b Standard Normal Distribution Tables (Example 3) Example 3: Find the value of k if (a) P (Z > k) = 0.0480 (b) P (Z > k) = 0.8350 Solution: (a) From the standard normal distribution table, k = 1.665 Z 6 5 (Subtract) 1.6 .0485 5 (b)   From the standard normal distribution table, k = –0.974 … Read more

5.2b Standard Normal Distribution Tables (Example 2) Example 2: Find the value of each of the following probabilities by reading the standard normal distribution tables. (a) P (0.4 < Z < 1.2) (b) P (–1 < Z < 2.5) (c) P (–1.3 < Z < –0.5) Solution: (a) P (0.4 < Z < 1.2) = … Read more

5.2b Standard Normal Distribution Tables (Example 1) Example 1: Find the value of each of the following probabilities by reading the standard normal distribution tables. (a) P (Z > 0.600) (b) P (Z < –1.24) (c) P (Z > –1.1) (d) P (Z < 0.76)   Solution: Standard Normal Distribution Table *When reading the standard normal distribution tables, it … Read more