Question

3. The daily surface concentration of carbonyl sulfide on the Indian Ocean is normally distributed, with a mean of 9.1 picomoles per liter and a standard deviation of 3.5 picomoles per liter. Find the probability that on a randomly selected day, the surface concentration of carbonyl sulfide on the Indian Ocean is less than 13.5 picomoles per liter.

Answer 1

Answer:  0.8956

Step-by-step explanation:

Given: The daily surface concentration of carbonyl sulfide on the Indian Ocean is normally distributed, with a mean $\mu=100$ picomoles per liter and standard deviation of $\sigma=3.5$ picomoles per liter.

Let X be the daily surface concentration of carbonyl sulfide.

The probability that on a randomly selected day, the surface concentration of carbonyl sulfide on the Indian Ocean is less than 13.5 picomoles per liter $= P(X<13.5)$

$=P(\dfrac{X-\mu}{\sigma}>\dfrac{13.5-9.1}{3.5})\\\\=P(Z<1.257)\\\\= 0.8956\ \ \ [\text{By p-value table}]$

Hence, the required probability =  0.8956