Struggling to figure these out, I have tried on my own a few times and have yet to get an answer that is remotely close to the correct one or what would be correct. In answer please include all steps
1) It is estimated that $17\%$ of cars are black. In a sample of $150$ cars, what is the probability that less than $20$ will be black?
2) It is estimated that $7\%$ of cars are blue. in a sample of $50$ cars, what is the probability that more than $10$ are blue?
I have tried to solve for if no black cars and then subtract it from one to get the total for black cars but that didn’t work. I did a bunch of the ways we did in class but none of them seem to work, one of the ways I tried got me a negative number which is not possible for these. I have been attempting by using the formula $\displaystyle P(x=k) = \binom{n}{k} p^k q^{n-k}$
I am not $100\%$ sure what the answer is, we weren’t given it to be able to check. I have been trying this for a few hours now and haven’t made a dent. This is for an online class and the teacher is no help. I am not sure how to do a sum of all the binomials that won’t take a million year with writing every single one out. Is their a short form? I don’t understand this.
That video is not what we have learned so far And we have used tables in the past but not yet for this.
For calculating an exact answer by hand, take the complement (i.e. probability 10 or fewer cars are blue): $$\sum_{k=0}^{10}\binom{50}k(0.07)^k(0.93)^{50-k}$$ This works out to $0.9994285$. The desired probability is $1$ minus this or $5.7148×10^{-4}$.