Exercise 3-59 Algo

Observations are drawn from a bell-shaped distribution with a mean of 210 and a standard deviation of 5. There are 1,900 observations in the data set.

a. Approximately what percentage of the observations are less than 220? (Round your answer to 1 decimal place.)



b. Approximately how many observations are less than 220? (Round your answer to the nearest whole number.)

1 answer

a. To find the percentage of observations that are less than 220, we need to find the area under the bell-shaped distribution curve to the left of 220.

To do this, we can use a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can find the z-score corresponding to a value of 220:
z = (x - mean) / standard deviation
z = (220 - 210) / 5
z = 2

Looking up the z-score of 2 in the standard normal distribution table, we find that the area to the left of 2 is approximately 0.9772.

So, approximately 97.7% of the observations are less than 220.

b. To find the approximate number of observations that are less than 220, we can multiply the percentage from part a by the total number of observations.

Approximately, 97.7% * 1,900 = 1,853 observations are less than 220.