Question

The weight of oranges growing in an orchard is normally distributed with a mean weight of 8 oz. and a standard deviation of 0.5 oz. Fill in the normal curve below with values for µ and σ, and label each interval, based on the normal approximation of those values.

Answer 1

The normal curve values based on the given mean and standard deviation can be determined using specific intervals.

Step-by-step explanation:

The given question is asking for the normal curve values based on the assumption that the weight of oranges in an orchard follows a normal distribution with a mean weight of 8 oz. and a standard deviation of 0.5 oz.

The normal curve can be filled in using the values of µ (mean) and σ (standard deviation) as follows:

• The interval to the left of the mean (µ - σ) includes 34.1% of the data.
• The interval between the mean and one standard deviation above the mean (µ + σ) includes 34.1% of the data.
• The interval between one standard deviation below the mean and one standard deviation above the mean (µ - σ to µ + σ) includes 68.2% of the data.
• The interval between two standard deviations below the mean and two standard deviations above the mean (µ - 2σ to µ + 2σ) includes 95.4% of the data.
• The interval between three standard deviations below the mean and three standard deviations above the mean (µ - 3σ to µ + 3σ) includes 99.7% of the data.