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It is known that 60% of customers will need additional maintenance on their vehicle when coming in for an oil change. A random sample of 48 customers is taken. What is the probability that more than 70% of customers in the sample will need additional maintenance

User Heez
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4 votes

Answer:

the probability that more than 70% of customers in the sample will need additional maintenance is 0.0371

Explanation:

From the information given:

we are to determine the probability that more than 70% of customers in the sample will need additional maintenance

In order to achieve that, let X be the random variable that follows a binomial distribution.

Then X
\sim Bin(48, 0.6)

However 70% of 48 samples is

= 0.7 × 48 = 33.6
\simeq 34

Therefore, the required probability is:

= P(X> 34)


= \sum \limits ^(48)_(x=34) (^(48)_(x)) (0.6)^x(1 - 0.6)^(48-x)


= (48!)/(34!(48-34)!) (0.6)^(34) (0.4)^(48-34)


= 4.823206232 * 10^(11) (0.60)^(34)(0.4)^(14)

= 0.03709524328


\simeq 0.0371

User Romarie
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