problem 1) Following data represent the life (in months) of 20 UPS fitted to a hospital on February, 25, 2005:

85    75    66    43    40
88    80    56    56    67
89    83    65    53    75
87    83    52    44    48

a) Construct frequency distribution with classes 40–49, 50–59, etc.

b) find out the sample mean from the frequency distribution, and interpret.

c) find out the sample mean from the raw data.

d) Compare parts (b) and (c) and comment on your answer.

problem 2) Here are the high temperature (in Fahrenheit) readings:

84    86    78    69    94    95    94    98    89    87    88
89    92    99   102   94    92    96    89    88    87    88
84    82    88    94    97    99    102    105

find out and interpret the:

a) Mean and median for this data

b) Standard deviation and variance

c) Interquartile range

d) 70th percentile   

problem 3)a) Define and describe mutually exclusive, not mutually exclusive, independent and dependent events.

b) Describe with exs the terms: permutation and combination.

c) A bag contains 5 white and 7 black balls. If three balls are drawn from the bag, what is the probability that;

i) All are white

ii) Two white and one black

iii) All are of the same color    

problem 4)a) The probability that married man watches a certain television show is 0.4 and the probability that a married woman watches the show is 0.5. The probability that a man watches the show, given that his wife does, is 0.7. Determine the probability that:

i) a married couple watches the show;

ii) a wife watches show given that her husband does;

iii) at least 1 person of a married couple will watch the show.

b) A town has 2 fire engines operating independently. Probability that specific engine is available when needed is 0.96.

i) Find the probability that neither is available when needed?

ii) Find the probability that a fire engine is available when needed?   

problem 5)a) A random sample of 100 recorded deaths during the past year showed an average life span of 71.8 years. Assuming a population standard deviation of 8.9 years, does this seem to indicate that mean life span today is great than 70 years? Use 0.05 level of significance.

b) Electric firm manufactures light bulbs that have lifetime that is approximately normally distributed with means of 800 hours and standard deviation of 40 hours. Test hypothesis that µ = 800 hours against alternative µ ≠ 800 hours if random sample of 30 bulbs has the average life of 788 hours. Use a 0.10 level of significance.