Question

Please explain and show all work

3· Le t x represent the number of credit cards a student has. A random sample of 100 students at a large university was taken and the results are in the table below: Credit NumberRelative xStudentsPr) 12 P(x) Cards of Frequencyx .P(x) 45 25 10 TOTAL 100 1.00 a) Construct a probability distribution histogram and comment on its shape b) What is the probability a randomly selected student has at least two credit cards? e) What is the probability a randomly selected student has at most three credit cards? d) What is the mean (round to one decimal place) of the probability distribution? e Given the standard deviation of the probability distribution is 1.1 credit cards, using the "range rule of thumb" (two standard deviation method) would it be unlikely for a household to have four credit cards? Explain

Answer 1

Credit Crads Number of Students Relative Fr P(x) x"P(x) 0-12-0 0.45 0.45 20.25 0.50 3 0.10-0.30 4 0.08-0.32 2 0+ 45+.50+.30+.32 1.57 0.5 0.45 04 0.35 0.3 0.45 12 45 25 10 -12/100 0.12 45/100-0.45 #25/100-0.25 10/100-0.10 -8/100 0.08 0.25 TOTAL 100 0.2 0.15 0.1 0.05 x*P(x) 0.12 0.1 0.12 0.45 0.25 0.1 0.08 a) The histogram seems to follow a normal distribution b) atleast 2 credits PI2)+ P(3) P(4) 0.43 c) atmost 3 credits 0.92 d) Mean I x*P(x)1.57 e) Yes it seems unlikely because the emprical rule clearly states that 2 standard deviations away from the mean covers 99.7% of observations and mean 157 is more than 2 S.D(1.1) way from 4