Question

A company produces bags of sugar whose masses in grams can be modeled by a normal distribution with a mean of 1000 and a standard deviation of 3.5. What is the probability that a randomly selected bag of sugar has a mass less than 996 grams?

A) 0.2119
B) 0.7881
C) 0.5
D) 0.2881

Answer 1

To find the probability that a randomly selected bag of sugar has a mass less than 996 grams, we need to calculate the z-score and then use the standard normal distribution table.

Step-by-step explanation:

To find the probability that a randomly selected bag of sugar has a mass less than 996 grams, we need to calculate the z-score and then use the standard normal distribution table.

The z-score is calculated using the formula: z = (x - mean) / standard deviation

For this problem, x = 996, mean = 1000, and standard deviation = 3.5.

Substituting these values into the formula, we get: z = (996 - 1000) / 3.5 = -1.142857

Now, we can use the standard normal distribution table to find the probability that a z-score is less than -1.142857. The table shows that this probability is approximately 0.1251.

Therefore, the probability that a randomly selected bag of sugar has a mass less than 996 grams is approximately 0.1251.