A local veterinary clinic typically sees 15% of its horses presenting with West

Question

A local veterinary clinic typically sees 15% of its horses presenting with West Nile virus. Last month, 100 horses were admitted and it was found that 20 of them had been infected with West Nile virus. The probability of seeing 20 or more horses with West Nile virus was calculated based on a Normal distribution with = 15 and standard deviation = 12.75. Which statement is TRUE?

All of the above

Using the Normal approximation to the binomial is justified because np = 15 and n(1 – p) = 85.

Using the Normal approximation to the binomial is justified because n is large and exact calculations are too tedious.

Using the Normal approximation to the binomial distribution is justified because X = 20 > 10.

Explanation / Answer

Solution:

Answer:

All of the above

Explanation:

We are given n = 100 and p = 0.15

We use normal approximation to binomial distribution if n*p>5 and n*q>5, where q = 1 – p

We have n*p = 100*0.15 = 15 > 5

And q = 1 – p = 1 – 0.15 = 0.85, n*q = 100*0.85 = 85 > 5

Here, n*p>5 and n*q>5,

So we can use normal approximation to binomial distribution.

Also, n is very large and calculations are too tedious.

Also, X = 20 > 10, calculations for X > 10 are very lengthy and we avoid it by using normal approximation.

So, all options are correct.

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