Statistics and Probability Answers

1.    Scores on BMCC fall 2017 MAT150.5 department final exam form a normal distribution with a mean of 70 and a standard deviation of 8. What percent of the population has the following? 

a.    A score greater than 90

b.    A score between 60 and 85

c.    A score less than 60

The probability of a man hitting a target is 0.40. If he fires 5 times then, find the probability of hitting the target, (a) exactly 3 times, (b) at least 4 times

two bags each contain ten discs which are indistinguishable apart from their colour. The first bag contains 4 red and 6 black discs and the second, 7 red and 3 black discs. A disc is chosen at random from the first bag and placed in the second. bag and placed in the first. Find the probability that the first bag still contains exactly 4 red discs?

A shipment of six laptops contains two that are slightly defective.If a retailer receives four of these laptops at random,list the elements of the sample space using the letters D and N for defective and non defective laptops, respectively.To each sample point assign a value x of the random variable x representing the number of laptops purchased by the retailer which are non defective.Construct a probability distribution for the random variable x by filling in the table below and draw it's corresponding histogram

Assume that 5% of Samsung's total smartphone production is defective. What is the probability that at least three of the smartphones are defective if ten items are chosen at random from the production line?

Mwema plays a game in which a fair die is thrown once. If the score is 1,2or 3 Mwema loses £10. If the score is 4 or 5 Mwema wins £x..If the score is 6, Mwema wins £2x.

      (i) Show that the expectation of Mwema’s is£ ( in a single game

The Head of the Math Department announced that the mean score of Grade 9 students in the first periodic examination in Mathematics was 89 and the standard deviation was 12. One student who believed that the mean score was less than this, randomly selected 34 students and computed their mean score. She obtained a mean score of 85. At 0.01 level of significance, test the student’s belief.

Two balls are drawn in succession without replacement from an urn

containing 5 white balls and 6 black balls. Let B be the random variable

representing the number of black balls. Construct the probability distribution

of the random variable B.

A meeting of envoys was attended by 4 Koreans and 2 Filipinos. If three

envoys were selected at random one after the other, determine the values

of the random variable F representing the number of Filipinos.

The median and the mode of the following distribution are known to be 27 and 26 respectively.

Class 0-10 10-20 20-30 30-40 40-50

Frequency 3 a 20 12 b

(i) Determine the values of a and b.                              (5 Marks)

(ii) Compute the arithmetic mean and the standard deviation of the distribution.