Question

PROBLEM SOLVING Scientists conducted aerial surveys of a seal sanctuary and recorded the number x of seals they observed during each

survey. The numbers of seals observed were normally distributed with a mean of 73 seals and a standard deviation of 14.1 seals. Find the
probability that at most 50 seals were observed during a randomly chosen survey.
The probability is
????????

Answer 1

Probability that at most 50 seals were observed during a randomly chosen survey is 0.0516.

Explanation:

We are given that Scientists conducted aerial surveys of a seal sanctuary and recorded the number x of seals they observed during each survey.

The numbers of seals observed were normally distributed with a mean of 73 seals and a standard deviation of 14.1 seals.

Let X = numbers of seals observed

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

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

where,
`\mu` = population mean numbers of seals = 73

`\sigma` = standard deviation = 14.1

Now, the probability that at most 50 seals were observed during a randomly chosen survey is given by = P(X
`\leq` 50 seals)

P(X
`\leq` 50) = P(
`(X-\mu)/(\sigma)`
`\leq`
`(50-73)/(14.1)` ) = P(Z
`\leq` -1.63) = 1 - P(Z < 1.63)

= 1 - 0.94845 = 0.0516

The above probability is calculated by looking at the value of x = 1.63 in the z table which has an area of 0.94845.