Final answer:
To determine the number of numbers expected to be less than 5 or greater than 45, we need to calculate the probability of a number falling outside of this range. By standardizing the values and using the z-score table, we can find the probabilities and multiply it by the number of samples.
Step-by-step explanation:
The number of numbers that are expected to be less than 5 or greater than 45 can be determined by calculating the probability of a number falling outside of this range.
First, we need to standardize the values of 5 and 45 using the formula z = (x - mean) / standard deviation, where z is the z-score, x is the value, mean is the mean of the distribution, and standard deviation is the standard deviation of the distribution.
Using the z-score table, we can find the probabilities corresponding to the z-scores of -2.33 (for 5) and 3.33 (for 45). Subtracting the probability corresponding to -2.33 from 0.5 (the probability below the mean) and adding the probability corresponding to 3.33 gives us the probability of a number being less than 5 or greater than 45. Finally, multiplying this probability by 1000 (the number of samples) will give us the expected number of numbers that fall outside of the range.