A food processor packages orange juice in small jars The weights of the filled are approximately normally distributed with a mean 10.5 ounces and standard deviation 0.3 ounce Find p?

Since the weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounces, we can use the standard normal distribution (z-distribution) to find the probability of a jar having a weight between 10 and 11 ounces.

Let X be the random variable representing the weight of a filled jar. Then, X ~ N(10.5, 0.3).

We want to find P(10 < X < 11).

First, we standardize the values using the formula z = (X - mu)/sigma, where mu is the mean and sigma is the standard deviation.

For X = 10, z = (10 - 10.5)/0.3 = -1.67

For X = 11, z = (11 - 10.5)/0.3 = 1.67

Now, we can use a standard normal distribution table or calculator to find the probabilities.

P(10 < X < 11) = P(-1.67 < z < 1.67) = 0.9044 - 0.0475 = 0.8569

Therefore, the probability of a jar having a weight between 10 and 11 ounces is approximately 0.8569.