Data are drawn from a bell-shaped distribution with a mean of 25 and a standard deviation of 4. There are 1.000 observations in the data set.
a. Approximately what percentage of the observations are less than 33? (Round your answer to 1 decimal place.)
b. Approximately how many observations are less than 33?

a) 97.7%

b) Approximately 977 of these observations are less than 33.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

a. Approximately what percentage of the observations are less than 33? (Round your answer to 1 decimal place.)

This is the pvalue of Z when X = 33. So

has a pvalue of 0.977

So 97.7% of the observations are less than 33.

b. Approximately how many observations are less than 33?

97.7% of 1000. So

0.977*100 = 977.

Approximately 977 of these observations are less than 33.

the balance is found at the link

step-by-step explanation:

the 3rd option is right

step-by-step explanation: