Question

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 76% 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 #1

**Solution:-**

p = 0.76

**a) The probability that within 2 years 47 or more fail
is 0.58284.**

x = 47

By applying binomial distribution:-

P(x,n) =
^{n}C_{x}*p^{x}*(1-p)^{(n-x)}

**P(x >
47) = 0.58284.**

**b) The probability that within 2 years 58 or fewer fail
is 0.000283.**

x = 58

By applying binomial distribution:-

P(x,n) =
^{n}C_{x}*p^{x}*(1-p)^{(n-x)}

**P(x >
58) = 0.000283.**

**c) The probability that within 2 years 15 or more
succeed is 0.5347.**

p = 1 - 0.76 = 0.24

By applying binomial distribution:-

P(x,n) =
^{n}C_{x}*p^{x}*(1-p)^{(n-x)}

**P(x >
15) = 0.5347**

**d) The probability that within 2 years fewer than 10
succeed is 0.04935.**

p = 0.24

By applying binomial distribution:-

P(x,n) =
^{n}C_{x}*p^{x}*(1-p)^{(n-x)}

**P(x < 10) = 0.04935**

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