Statistics & Probability 2 Supplemental Problems

Statistics & Probability 2 Supplemental Problems

Math MethodsName______

Chapter 13, 16-17

Statistics & Probability 2 Supplemental Problems 

  1. Draw a frequency diagram using intervals of five beginning at 0 (show the frequency table):

12 14 24 22 18 7 4 8 19 21 13 3 18 1 10 8 6 11 14 20 5 2 15 19 21 7 8

  1. Find the mean (no 1-var stat)
  1. Using your calculator find the mean, median and mode correct to three significant figures:

12.8 9 14 2.6 7.2 6.8 6.8 5.9 12.8 4.8 19.4

  1. Find the quartiles and draw a box-and-whisker plot: 19 43 91 59 83 62 77 14 82 53 22
  1. Find the standard deviation (do not use 1-var stat) correct to three significant figures:

4 6 2 5 8 1 9 4

  1. Find the standard deviation (do not use 1-var stat) of #2.
  1. Consider the following set of data:

12, 4, 9, 10, 12, 13, 15, 11, 12, 15, 14, 8, 9, 10, 12, 9, 10, 16, 14, 13, 12, 15, 9, 10, 12

  1. Construct a cumulative frequency table and curve
  2. From the curve, determine the median and quartiles
  3. Calculate the interquartile range
  1. Using a normal table, find

i. ii. iii.

  1. A brand of tinned baked beans have a mean contents of 345 grams per tin with a standard deviation of 2.8 grams. Assuming that the distribution is normal, what percentage (to the nearest whole number) of the tins contain:
  1. less than 347 grams
  2. more than 345.5 grams
  3. between 343 and 346 grams

If the lightest 1% of the cans are considered to be underweight:

  1. find the weight below which the cans are considered underweight
  1. As a result of a certain random experiment, the events A and/or B may occur. These events are independent, and
  1. Let X denote the random variable which counts how many of the two events occur at a given time. Thus, for example, if neither A nor B occur. Find for
  2. Find the mean and variance of X
  1. A certain brand of soft-drink is sold in so-called ‘litre’ bottles. In fact, the amount of liquid in each bottle (in litres) is a normally distributed random variable with mean 1.005 and standard deviation of 0.01.
  1. Find the proportion of soft-drink bottles containing less than 1 litre
  2. If I buy four bottles, find the probability that all four contain less than 1 litre
  1. A bag contains 3 red and 2 black marbles. Let X be the number of marbles withdrawn (at random), one at a time without replacement, until the first black marble is drawn.
  1. Explain why X cannot take any value greater than 4
  2. Specify the probability distribution of X
  3. Find i. ii. iii.
  1. A discrete random variable X may take the values 0, 1, or 2. The probability distribution of X is defined by . FindK
  1. The cross-sectional area of a rod produced by a machine is normally distributed with a standard deviation of and a mean of .
  1. If the proportion of rods with cross-section area of less than 3.0 is 0.04, evaluate .
  2. If all rods with cross-sectional area of less than 3.0 are rejected, what is the probability of an accepted rod having a cross-sectional area greater than 5 ?
  1. The mean diameter of bolts from a machine can be adjusted so that the proportion of bolts greater than 1.00 cm is 0.05, and the proportion less than 0.90 cm is 0.01. Assuming the distribution of the bolt diameters to be Normal, find the mean and the standard deviation of the diameter.
  1. Of 5 cards, 3 are labeled with a 1, the others with a 2. Three cards are drawn at random from the five cards, observed, then returned to the pack. This process is repeated a second time. If X denotes the number of times two 1’s and a 2 are drawn,
  1. Find the probability of two 1’s and a 2 on the first draw.
  2. Find , for for the two draws
  3. Calculate the mean and variance of X
  4. Calculate
  1. A tennis player find that he wins 5 out of 7 games he plays. If he plays 7 games straight, find the probability that he will win
  1. Exactly 3 games
  2. At most 3 games
  3. All 7 games
  4. No more than 5 games
  5. After playing 30 games, how many of these would he expect to win?
  1. If X~N(50, 25) find
  2. c if
  1. the end

ANSWERS:

ANSWERS:

1. 2. 62.9 3. 4.

5. 2.57 6. 7.70

8a. .0005 8b. .7393 8c. .119 9i. .7625 9ii. .4291 9iii. .4020 9iv. 338 10a.

10b. Mean: .7 Variance: .41 11a. .3085 11b. .0091 12a. only 3 reds 12b.

12ci. 2 12cii. 5 12ciii. 3 13. 14a. .5712 14b. .04

15. Mean= .959 SD= .025

16a. 16b. 16c. mean 1.2, var .48 16d. 17a. .085 17b. .108

17c. .095 17d. .64 17e. 21 18a. .1391 18b. 41.5

MM Ch13, 16-17 Supplemental Problems.09

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