a. To determine the percentage of observations that are less than 46, we can use the standard normal distribution.
First, we need to calculate the z-score for 46 using the formula:
z = (x - μ) / σ
where x is the value we are interested in (46), μ is the mean (40), and σ is the standard deviation (3).
z = (46 - 40) / 3
z = 2
Next, we can use a standard normal distribution table or a calculator to find the area under the curve to the left of z = 2.
Looking up the z-score of 2 in a standard normal table, we find that the area to the left of z = 2 is approximately 0.9772.
Therefore, approximately 97.72% of the observations are less than 46.
b. To determine the approximate number of observations that are less than 46, we can multiply the percentage found in part a by the total number of observations (300).
Approximate number of observations = Percentage of observations * Total number of observations
Approximate number of observations = 0.9772 * 300
Approximate number of observations = 293.16
Approximately 293 observations are less than 46. (Rounded to the nearest whole number: 293)
Observations are drawn from a bell-shaped distribution with a mean of 40 and a standard deviation of 3. There are 300 observations in the data set.
a. Approximately what percentage of the observations are less than 46? (Round your answer to 1 decimal place.)
b. Approximately how many observations are less than 46? (Round your answer to the nearest whole number.)
1 answer
1 answer