Question

A Niffler is a magical creature who loves to collect shiny objects and store them in their pouch, much like a kangaroo. The amount a Niffler can hold in their pouch is approximately normally distributed with a mean of 25 pounds of shiny objects and a standard deviation of 6.8 pounds. Newt Scamander, while studying magical creatures in Britain, found a new colony of Nifflers. He discovered a Niffler who had 32 pounds in their pouch. What is the probability that a Niffler can hold more than 32 pounds of shiny objects in their pouch?

Answer 1

Probability that a Niffler can hold more than 32 pounds of shiny objects in their pouch is 0.1515.

Explanation:

We are given that the amount a Niffler can hold in their pouch is approximately normally distributed with a mean of 25 pounds of shiny objects and a standard deviation of 6.8 pounds.

Let X = amount a Niffler can hold in their pouch

So, X ~ Normal(
`\mu=25,\sigma^(2) =6.8^(2)`)

The z score probability distribution for normal distribution is given by;

Z =
`(X-\mu)/(\sigma)` ~ N(0,1)

where,
`\mu` = population mean = 25 pounds

`\sigma` = standard deviation = 6.8 pounds

Now, the probability that a Niffler can hold more than 32 pounds of shiny objects in their pouch is given by = P(X > 32 pounds)

P(X > 32 pounds) = P(
`(X-\mu)/(\sigma)` >
`(32-25)/(6.8)` ) = P(Z > 1.03) = 1 - P(Z
`\leq` 1.03)

= 1 - 0.8485 = 0.1515

The above probability is calculated by looking at the value of x = 1.03 in the z table which has an area of 0.8485.

Hence, the probability that a Niffler can hold more than 32 pounds of shiny objects in their pouch is 0.1515.