Question

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.963 grams and a standard deviation of 0.308 grams. Find the probability of randomly selecting a cigarette with 0.501grams of nicotine or less. Round your answer to four decimals.

P (X<0.501) = ?

Answer 1

Using the standard normal distribution, we can calculate the probability of randomly selecting a cigarette with 0.501 grams of nicotine or less by converting it to a standard score (z-score) and using a normalcdf function. The probability is approximately 0.0672.

Step-by-step explanation:

To find the probability of randomly selecting a cigarette with 0.501 grams of nicotine or less, we need to use the standard normal distribution and convert the given value to a standard score (z-score). The formula to calculate the standard score is:

z = (x - mean) / standard deviation

In this case, x = 0.501 grams, mean = 0.963 grams, and standard deviation = 0.308 grams.

Substituting these values into the formula:

z = (0.501 - 0.963) / 0.308 = -1.4922

To find the probability, we can use a standard normal distribution table or a calculator with a normalcdf function.

Using the normalcdf function with a lower bound of -infinity and an upper bound of -1.4922, we can calculate the probability:

P(X < 0.501) = normalcdf(-infinity, -1.4922) = 0.0672

Rounding this answer to four decimals, the probability of randomly selecting a cigarette with 0.501 grams of nicotine or less is approximately 0.0672.