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Consider a binomial experiment with n=20 and p=0.70.

Find f(12). Find f(16). Find $P(x ge 16)$. Find $P(x le 15)$. Find $E(x)$. Find $var(x)$ and $sigma$. The main objective of this question is to find the binomial probability. This question uses the concept of the binomial distribution to find the binomial probability. In binomial distribution, we have the probability of two possible outcomes […]

Can two events with nonzero probabilities be both independent and mutually exclusive?

The question aims to answer if two events can be both independent and mutually exclusive simultaneously with non-zero probabilities. When we toss two coins, the result of one coin does not affect the other. if one outcome is head/tail, this doesn’t affect the result of another event. This means mutually exclusive events are not independent. […]

A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs?

 – In existing experimentation, $100$ customers were asked to choose the design they liked. The subsequent data were acquired. Do the data demonstrate the thought that one design is just as conceivable to be designated as another? Explain. This problem aims to familiarize us with the concept of the null hypothesis and probability distribution. The […]