In a memory test, the test subjects are shown 300 objects and are asked after two hours to name the objects. The historical records show that test subjects remember 75% of the objects after two hours. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p, where p is the proportion of objects that are remembered by a test subject. ? (b) Find the standard deviation of p. |(c) Compute an approximation for P(p <0.79), which is the probability that fewer than 79% of the objects are remembered by a test subject. Round your answer to four decimal places.

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### Memory Test Analysis

In a memory test, the test subjects are shown 300 objects and are asked after two hours to name the objects. The historical records show that test subjects remember 75% of the objects after two hours.

**Answer the following: (If necessary, consult a [list of formulas](#)):**

#### (a) Find the mean of \( \hat{p} \), where \( \hat{p} \) is the proportion of objects that are remembered by a test subject.
\[ \quad \]

#### (b) Find the standard deviation of \( \hat{p} \).
\[ \quad \]

#### (c) Compute an approximation for \( P(\hat{p} < 0.79) \), which is the probability that fewer than 79% of the objects are remembered by a test subject. Round your answer to four decimal places.
\[ \quad \]

### Notes on Graphs/Diagrams:
There are no graphs or diagrams provided in this explanation. If there were, they would be used to visually illustrate data distributions, standard deviations, or probability calculations related to the test subjects' memory performance.
Transcribed Image Text:### Memory Test Analysis In a memory test, the test subjects are shown 300 objects and are asked after two hours to name the objects. The historical records show that test subjects remember 75% of the objects after two hours. **Answer the following: (If necessary, consult a [list of formulas](#)):** #### (a) Find the mean of \( \hat{p} \), where \( \hat{p} \) is the proportion of objects that are remembered by a test subject. \[ \quad \] #### (b) Find the standard deviation of \( \hat{p} \). \[ \quad \] #### (c) Compute an approximation for \( P(\hat{p} < 0.79) \), which is the probability that fewer than 79% of the objects are remembered by a test subject. Round your answer to four decimal places. \[ \quad \] ### Notes on Graphs/Diagrams: There are no graphs or diagrams provided in this explanation. If there were, they would be used to visually illustrate data distributions, standard deviations, or probability calculations related to the test subjects' memory performance.
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