Question

The lengths of salamanders have a normal distribution with mean 15cm, and standard deviation 2cm. In a collection of 300 salamanders, about how many have length greater than 16.8cm? (round answers to the nearest hundredth and show your work in the sketch area at left)

Answer 1

Answer:

55.22 salamanders

Step-by-step explanation:

Z score formula is given as:

Z score = x - μ/σ

x = 16.8 cm

μ = mean = 15cm

σ = standard deviation 2cm

Z score = 16.8 - 15/2

= = 0.9

Probability value from Z-Table:

P(x<16.8) = 0.81594

P(x>16.8) = 1 - P(x<16.8)

1 - 0.81594

= 0.18406

In a collection of 300 salamanders, about how many have length greater than 16.8cm?

= 300 × 0.18406

= 55.218 salamanders

Approximately to the nearest hundredth = 55.22 salamanders

Therefore, 55.22 salamanders have length greater than 16.8cm