Chapter 13.1, Problem 81E

Dungeons and Dragons: Part A A 20-sided die is often used in tabletop role-playing games like Dungeons and Dragons.  During the game players may face something called a "skill check" where they must roll a 20-sided die and get a result equal to or above a given value.  For example, a player may be required to roll a 15 or above in order to succeed and pass the skill check.  Rolling a 14 or lower would be a failure.  If the player rolls the die 10 times in a row, what is the expected number of rolls that would pass the skill check by rolling as a 15 or higher? For the previous calculations, what is the standard deviation for the number of times the die would be rolled 15 or above During a game of Dungeons and Dragons, the previously-mentioned player rolls the 20-sided die 30 times in total.  What is the probablity that they successfully roll a 15 or higher exactly 7 times during that game? Express your final answer as a percentage to 2 decimal places.

Q3. The distribution for the working lifetime of light bulbs, manufactured in a company, is found to be normally distributed with a mean of 1450 hours and a standard deviation of 60 hours. a) In this distribution, find the life time of a lightbulb whose z-score is -1.8? b) Which percentage of lightbulbs have life time less than 1400 hours? c) Which percentage of lightbulbs have life time greater than 1500 hours? d) Which percentage of lightbulbs have life time between 1420 to 1500 hours?

Q4. Considering the following two normal distributions A and B, which statement (or statements) is correct? a) Mode of the distribution A is larger than that of distribution B. b) SD of the distribution B is larger than that of distribution A. c) Mean of the distribution A is smaller than that of distribution B. d) A data item with z-score of -1 falls between 20 to 30 in distribution A. e) A data item with z-score of +1 falls between 10 to 20 in distribution B. A 0 10 20 30 40 40 50 60 00 10 70 B 80 90 100