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Self-assessment exam C Probability Distributions - answers Binomial-Poisson-Normal-Sampling distribution of the mean Name: ____________________________ 1-2. Complete: a) In a binomial distribution with n=400 and p=0.3, the mean =___120_____ b) In a binomial distribution with n=400 and p=0.3, the standard deviation =_9.16515139______ c) The mean of the standard normal distribution is ___0____. d) The standard deviation of the standard normal distribution is __1______. e) The only parameter of the Poisson distribution is ______p___ f) The parameter of the geometric distribution is __mean______ g) In the standard normal distribution the z-value below which we have a 40% probability is _-0.253347___ invNorm(0.40)= -0.253347 h) In a standard normal distribution, the P(x>-1.43) = ___0.9236414449__________ normalcdf(-1.43, 10^9)= 0.9236414449 i) In a binomial problem with n=70, p=0.18, P(x> 12) = __0.4990102337_____ 1 - binomialcdf(70, 0.18, 12) = 0.4990102337 j) In a normal distribution with mean 40 and 3.5 , the ordinate at x=40 is 0.1139835087__ normalpdf(40, 40, 3.5) =0.1139835087 3. Five percent (5 %) of all TVs manufactured by a certain electronics company are defective. A quality control inspector randomly selects a sample of 40 TVs from the production line. What is the probability a) more than 2 of them are defective? Binomial: n=40, p=0.05, x>2 Answer: 1 - binomialcdf(40, 0.05, 2)= 0.3232642405 b) none of them are defective? Answer: binomialpdf(40, 0.05, 0) =0.1285121566 a 0.3232642405___ b) 0.1285121566 4. A washing machine In a Laundromat breaks down at an average of three times per month. Find the probability that during the next month this machine will have Poisson 3 breaks down per month a) at most 1 breakdowns Poissoncdf ( 3, 1)=0.1991482735 a) 0.1991482735 b) exactly 21 breakdowns Poissonpdp (3, 21) 1.01933982 10 b) -11 0.0000000000101933982 0.0000000000101933982 5. The probability that a baseball player hits a home run during a game is 0.15. Assuming that this probability remains the same for the whole baseball season, what is the probability that the player will hit his first home run after the 3rd game? Geometric: p=0.15, x>3 Answer: 1 - geometriccdf(0.15, 3) = 0.614125 answer: = 0.614125 -1- 6. In selecting at random sample of 5 students from a class of 30 students, what is the probability that the sample will be composed of 3 female students and 2 male students?. In the class there are 18 females students and 12 males students. Use the Hyper-geometric distribution. C C 816 66 P(x 3 females ) 18 3 12 2 0.3779209296 142506 30 C5 6. 0.3779209296 ___ 7. A normally distributed random variable x possesses a mean of 65 and a standard deviation of 3.4. Find the probability that a) a value of x falls between 62 and 66. a) _0.4268729858___ Answer: Normalcdf(62, 66, 65, 3.4) = 0.4268729858 b) Find the 60th. percentile of the distribution. Answer: InvNormal(0.60, 65, 3.4)= 65.86138014 b)_ 65.86138014__ 8. The grades for a large statistics class are normally distributed with mean of 64 and a standard deviation of 15.3. If the middle 40% of the class will receive C's in the exam, what are the lowest and highest C grade. Give answer rounded to one decimal place. Lowest C=55.9 Lowest C = invNormal (0.30, 64, 15.3) =55.9766722 8.__Highest C= 72.0___________ Highest C = invNormal (0.70, 64, 15.3) =72.0233278 9. In January 21, 1938, the temperature in San Fernando de la Torres was normally distributed with mean of 34 degrees and standard deviation of 2.5 degrees. What percentage of the time was the temperature above freezing, that is above 32 degrees Fahrenheit? Normalcdf(32, 10^9, 34, 2.5) = 0.7881446663 9. __78.81%______________ 10 5% of the production of a certain company is rejected due to too much alcohol, and has to be re-processed. It is known that the standard deviation for the milliliters of alcohol per bottle is 0.4 and that if a bottle contains more than 5 milliliters of alcohol, it is rejected. What is the average amount of alcohol per bottle? MATH 0 CLEAR ALPHA SOLVE X=4.3420586099 eqn: 0= normalcdf ( 5, 10^9, x, 0.4) - 0.05 ENTER x=make a good guess 10.____average is 4.34 milliliters per bottle. _ -2-