SOLUTION: In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

Click here to see ALL problems on Probability-and-statistics

Question 1142730: In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.
It is known that 83% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 62 new products, find the following probabilities. (Round your answers to four decimal places.)
(a) within 2 years 47 or more fail

(b) within 2 years 58 or fewer fail

(c) within 2 years 15 or more succeed

(d) within 2 years fewer than 10 succeed

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
mean is np=62*0.83=51.46
variance is np(1-p)=51.46*0.17=8.7482
sd is sqrt (V)=2.96
47 or more use 46.5 as continuity correction factor
z>(46.5-51.46)/2.96=-1.68
0.9535
58 or fewer use 58.5
(58.5-51.46)/2.96 or z<2.38 with probability of 0.9913
15 or more succeed is 47 or fewer fail
z< (47-51.46)/2.96=-1.51
that has probability of 0.0655
fewer than 10 succeed means no more than 9 do which means that at least 53 fail.
z>(53-51.46)/2.96 or z>0.52 0.3015 probability.