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 75% of all new products introduced in grocery
stores fail (are taken off the market) within 2 years. If a grocery
store chain introduces 60 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
here for binomial distribution parameter n=60 and p=0.75 
here mean of distribution=μ=np=  45.0000  
and standard deviation σ=sqrt(np(1p))=  3.3541  
for normal distribution z score =(Xμ)/σx  
since np and n(1p) both are greater than 5, we can use normal approximation of binomial distribution  
therefore from normal approximation of binomial distribution and continuity correction: 
a)

b)

c)
P( 15 or more succeed ) =P(at most 45 fail):
probability =P(X<45.5)=(Z<(45.545)/3.354)=P(Z<0.15)=0.5596 
d)
P( fewer than 10 succeed ) =P(at least 51 succeed):
probability =P(X>50.5)=P(Z>(50.545)/3.354)=P(Z>1.64)=1P(Z<1.64)=10.9495=0.0505 
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