Question

A researcher was interested in seeing how many names a class of 38 students could remember after playing a name game After playing the name game, the students were asked to recall as many first names of fellow students as possible. The mean number of names recalled was 19.41 with a standard deviation of 3.17. Use this information to solve the following problem.
What proportion of the students recalled less than 15 names?

a. .0823

b. .5823

c. .4177

d. .4923

Answer 1

A researcher was interested in seeing how many names a class of 38 students could remember after playing a name game.

After playing the name game, the students were asked to recall as many first names of fellow students as possible. The mean number of names recalled was 19.41 with a standard deviation of 3.17.

The above distribution is a normal distribution with mean 19.41 with a standard deviation of 3.17

For normal distribution,

Here is the formula for z-score that we will be using to calculate probabilities:

z is the "z-score" (Standard Score) x is the value to be standardized μ is the mean σ is the standard deviation

Let the number of names recalled by a student be denoted by x

Q)Find the probability that a randomly selected student recalls less than 15 names

Note: What is meant here by area is the area under the standard normal curve.

For x = 15, the z-value z = (15 - 19.41) / 3.17 = -1.3912
Hence P(x < 15) = P(z < -1.3912) = [area to the left of -1.3912] = 0.0823

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