Suppose the length of an oarfish is normally distributed with a mean of 6.5 m and a standard deviation of 1.5 m. Which group describes 16% of the oarfish population? Select each correct answer. oarfish that are between 6.5 m and 9.5 m oarfish that are shorter than 5 m oarfish that are between 3.5 m and 9.5 m oarfish that are longer than 8 m

Step-by-step explanation:

Let x be the random variable representing the length of an oarfish. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

The given probability value is 16% = 0.16. From the normal distribution table, the z score corresponding to the probability value is - 0.99

This indicates that the sample mean is lower than the population mean

Therefore,

- 0.99 = (x - 6.5)/1.5

- 0.99 × 1.5 = x - 6.5

- 1.5 = x - 6.5

x = - 1.5 + 6.5

x = 5m

The correct answer is

oarfish that are shorter than 5 m