what is the probability that a loaf of bread is between 22.75 and 23.00?
Incomplete information
To determine the probability that a loaf of bread is between 22.75 and 23.00, you need to know the distribution of bread weights and the range of possible weights.
1. Gather the data: Find information on the distribution of bread weights from a reliable source, such as bread manufacturers or industry reports. For simplicity, let's assume that the weights follow a normal distribution.
2. Assess the mean and standard deviation: Determine the mean (μ) and standard deviation (σ) of the bread weights from the available data. These parameters are crucial for calculating probabilities in a normal distribution.
3. Standardize the values: Convert the given weight range (22.75 to 23.00) into standardized z-scores. Subtract the mean from the lower and upper bounds of the range and divide by the standard deviation.
Lower z-score = (22.75 - μ) / σ
Upper z-score = (23.00 - μ) / σ
4. Look up probabilities from the standard normal distribution table: Once you have the z-scores, consult a standard normal distribution table (also known as a z-table) to find the probabilities associated with those z-scores. The table provides probabilities for different values of the standard normal distribution.
P(22.75 ≤ X ≤ 23.00) = P(Lower z-score ≤ Z ≤ Upper z-score)
5. Calculate the probability: Once you have the corresponding probabilities for the lower and upper z-scores from the z-table, subtract the lower probability from the upper probability to get the probability of a loaf of bread falling within the given weight range.
Probability = Upper probability - Lower probability
Note that the specific values for μ and σ will depend on the particular distribution of bread weights, so make sure to gather accurate data from a reliable source to obtain the most accurate probability calculation.