Question

consider the following probability distribution table for checking a random sample of new toyota automobiles for defective accelerators pedal which get stuck when you push down too hard. let x denote the number of these defective accelerators found when quality control engineers check a random sample of 10 new toyota cars for defective accelerator pedal. please answer the following four questions below.
probability distribution for new toyota automobiles
x: 0,1,2,3,4,5,6,7,8,9,10
p(x): 0.03,0.05,0.07,0.09,0.13,0.26,0.13,0.09,0.07,0.05,0.03
x·p(x): 0.00,0.05,0.14,0.27,0.52,1.30,0.78,0.63,0.56,0.45,0.30
#35 what is the sum of the row designated p(x) for the above probability distribution?
(a) 0.75 (b) 0.90 (c) 1.00 (d) 1.25 (e) none of these
#36 what is the population mean (μ) for the random variable x in the above table?
(a) 6.00 (b) 5.00 (c) 4.00 (d) 3.00 (e) none of these
#37 use the range rule of thumb to estimate the standard deviation (sd) for the random variable x in the above probability distribution table.
(a) 2.25 (b) 2.50 (c) 2.75 (d) 2.95 (e) none of these
#38 referring to the previous question #37, what is your estimate of the variance (var) for the random variable x in the above probability distribution table?
(a) 5.0625 (b) 6.250 (c) 7.5625 (d) 8.7025 (e) none of these
note: the small business administration estimates that 75% of new companies will eventually fail and go bankrupt within 5 years. if you take a random sample of 100 new companies, please answer the questions below.
#39 what type of probability distribution is described by this scenario?
(a) normal (b) poisson (c) binomial (d) none of these
#40 what percentage of new companies would you expect to succeed within 5 years?
(a) 20% (b) 25% (c) 75% (d) 80% (e) none of these
#41 what is the number (μ) of new small companies you’d expect to fail within 5 years?
(a) 60 (b) 70 (c) 75 (d) 80 (e) none of these
#42 what is the variance (var) for the number of companies that you’d expect to fail?
μ = n·p

Explanation:

First Section (Toyota Automobiles)

[35]

Step1: Sum P(X) values

Sum = 0.03+0.05+0.07+0.09+0.13+0.26+0.13+0.09+0.07+0.05+0.03 = 1.00

[36]

Step1: Calculate population mean

Mean = Sum(X·P(X)) = 0.00+0.05+0.14+0.27+0.52+1.30+0.78+0.63+0.56+0.45+0.30 = 6.00

[37]

Step1: Find range of X

Range = Max(X)-Min(X) = 10-0 = 10

Step2: Apply Range Rule of Thumb

SD ≈ Range/4 = 10/4 = 2.50

[38]

Answer:

C. 1.00