A soda production company fills cans that hold 12 ounces of soda. The actual amount of soda dispensed into each can is normally distributed with a mean of 11.9 oz. and a standard deviation of 0.02 oz. Use a calculator to find the probability that you find a can of soda with less than 11.87 oz.
To find the probability that you find a can of soda with less than 11.87 oz, we need to calculate the z-score first:
z = (X - μ) / σ
z = (11.87 - 11.9) / 0.02
z = -0.15
Next, we look up the z-score in a z-table or use a calculator to find the probability associated with this z-score. The probability of finding a can of soda with less than 11.87 oz is the area to the left of the z-score.
Using a calculator:
P(Z < -0.15) = 0.4404
Therefore, the probability of finding a can of soda with less than 11.87 oz is approximately 0.4404 or 44.04%.
is this right
I made a mistake in my calculations, I apologize for the error. Let's recalculate:
To find the probability of finding a can of soda with less than 11.87 oz, we will calculate the z-score as follows:
z = (X - μ) / σ
z = (11.87 - 11.9) / 0.02
z = -1.5
Now, we need to find the probability associated with a z-score of -1.5. Using a calculator or a z-table, we find that the probability is approximately 0.0668.
Therefore, the correct probability of finding a can of soda with less than 11.87 oz is approximately 0.0668 or 6.68%.