SOLUTION: Mathematics Business Statistics The Tea Delish Company claims that 40% of its customers The Tea Delish Company claims that 40% of its customers Need more help! The Tea Delish

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Question 1192904: Mathematics Business Statistics The Tea Delish Company claims that 40% of its customers
The Tea Delish Company claims that 40% of its customers
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The Tea Delish Company claims that 40% of its customers are between 35 to 45 years of age. In a random sample of 250 customers:
a. What is the probability that between 100 and 115 customers were in the 35 to 45 years age range?
b. What is the probability that more than 120 customers were in the 35 to 45 years age range?
c. What is the probability that fewer than 90 or more than 120 customers were in the 35 to 45 years age range?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
mean is np=100
variance is np(1-p)=60
sd is sqrt(V)=7.75
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between 100 and 115 is 99.5 to 115.5 using continuity correction factor for normal approximation
that is z=(99.5-100)/7.75=-0.06 and (115.5-100)/7.75=2. Probability is 0.5012
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more than 120 is z=(120.5-100)/7.75=2.645
z> 2.65 with probability of 0.0041
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fewer than 90 use (89.5-100)/7.75 for z<-1.355 for probability 0.0877
Adding that to the other probability, the answer is 0.0918.