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A television dealer has observed that 75% of all televisions that he sells are portable. Find...

A television dealer has observed that 75% of all televisions that he sells are portable. Find the approximate probability that, of the next 50 sets sold, at least 35 will be portable.

Math   Statistics-And-Probability   
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Answer #1

Let X be a random variable representing the number of portable television sets of the next 50 sets sold. Then X is a binomial random variable with n=50 and p=0.75

Here since n>30 so we use normal approximation of binomial distribution. That is if X is a binomial random variable with mean E(X) and variance Var(X) then

that is Z follows standard normal distribution.

Here

So,

the probability that at least 35 sets will be portable =

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