The reading speed of second grade students in a large city is approximately normal, with a mean of 91 words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f). Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (d) What effect does increasing the sample size have on the probability? Provide an explanation for this result. A. Increasing the sample size decreases the probability because o, decreases as n increases.

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**Text Transcription for Educational Website:**

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**The reading speed of second grade students in a large city is approximately normal, with a mean of 91 words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f).**

**Click here to view the standard normal distribution table (page 1).**  
**Click here to view the standard normal distribution table (page 2).**

---

**(d) What effect does increasing the sample size have on the probability? Provide an explanation for this result.**

- **A. Increasing the sample size decreases the probability because \(\sigma_{\bar{x}}\) decreases as \(n\) increases.**
  
- **B. Increasing the sample size increases the probability because \(\sigma_{\bar{x}}\) increases as \(n\) increases.**
  
- **C. Increasing the sample size decreases the probability because \(\sigma_{\bar{x}}\) increases as \(n\) increases.**
  
- **D. Increasing the sample size increases the probability because \(\sigma_{\bar{x}}\) decreases as \(n\) increases.**

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**(e) A teacher instituted a new reading program at school. After 10 weeks in the program, it was found that the mean reading speed of a random sample of 19 second grade students was 93.8 wpm. What might you conclude based on this result? Select the correct choice below and fill in the answer boxes within your choice.**

*(Type integers or decimals rounded to four decimal places as needed.)*

- **○ A. A mean reading rate of 93.8 wpm is not unusual since the probability of obtaining a result of 93.8 wpm or more is [.]. This means that we would expect a mean reading rate of 93.8 or higher from a population whose mean reading rate is 91 in [.] of every 100 random samples of size \(n = 19\) students. The new program is not abundantly more effective than the old program.**

- **○ B. A mean reading rate of 93.8 wpm is unusual since the probability of obtaining a result of 93.8 wpm or more is [.]. This means that we would expect a mean reading rate of 93.8 or higher from a population whose mean reading rate is 91 in [.] of every 100 random samples of size \(
Transcribed Image Text:**Text Transcription for Educational Website:** --- **The reading speed of second grade students in a large city is approximately normal, with a mean of 91 words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f).** **Click here to view the standard normal distribution table (page 1).** **Click here to view the standard normal distribution table (page 2).** --- **(d) What effect does increasing the sample size have on the probability? Provide an explanation for this result.** - **A. Increasing the sample size decreases the probability because \(\sigma_{\bar{x}}\) decreases as \(n\) increases.** - **B. Increasing the sample size increases the probability because \(\sigma_{\bar{x}}\) increases as \(n\) increases.** - **C. Increasing the sample size decreases the probability because \(\sigma_{\bar{x}}\) increases as \(n\) increases.** - **D. Increasing the sample size increases the probability because \(\sigma_{\bar{x}}\) decreases as \(n\) increases.** --- **(e) A teacher instituted a new reading program at school. After 10 weeks in the program, it was found that the mean reading speed of a random sample of 19 second grade students was 93.8 wpm. What might you conclude based on this result? Select the correct choice below and fill in the answer boxes within your choice.** *(Type integers or decimals rounded to four decimal places as needed.)* - **○ A. A mean reading rate of 93.8 wpm is not unusual since the probability of obtaining a result of 93.8 wpm or more is [.]. This means that we would expect a mean reading rate of 93.8 or higher from a population whose mean reading rate is 91 in [.] of every 100 random samples of size \(n = 19\) students. The new program is not abundantly more effective than the old program.** - **○ B. A mean reading rate of 93.8 wpm is unusual since the probability of obtaining a result of 93.8 wpm or more is [.]. This means that we would expect a mean reading rate of 93.8 or higher from a population whose mean reading rate is 91 in [.] of every 100 random samples of size \(
**Standard Normal Distribution Table (Page 1)**

This table provides the cumulative probabilities for the standard normal distribution (Z-distribution), which is a continuous probability distribution that has a mean of 0 and a standard deviation of 1.

**Diagram Explanation:**
At the top left of the table is a bell-shaped curve, representing the standard normal distribution. The shaded area under the curve signifies the cumulative probability corresponding to the Z-score.

**Table Explanation:**
- The Z-scores range from -3.4 to -0.1 in increments of 0.1.
- The table headers (0.00 to 0.09) represent the second decimal place of the Z-score.
- For example, a Z-score of -2.5 with a second digit of 0.04 corresponds to a cumulative probability of 0.0062.

**Standard Normal Distribution Table (Page 2)**

This continuation of the standard normal distribution table covers positive Z-scores, providing the cumulative probability for each.

**Diagram Explanation:**
Similarly, a bell-shaped curve appears, indicating the cumulative probability area to the left of the specified Z-score.

**Table Explanation:**
- The Z-scores range from 0.0 to 2.9 in increments of 0.1.
- The cumulative probabilities increase progressively since they represent areas under the curve as you move right on the Z-distribution.

Together, these tables are essential for calculating probabilities and understanding the properties of the normal distribution in various statistical analyses.
Transcribed Image Text:**Standard Normal Distribution Table (Page 1)** This table provides the cumulative probabilities for the standard normal distribution (Z-distribution), which is a continuous probability distribution that has a mean of 0 and a standard deviation of 1. **Diagram Explanation:** At the top left of the table is a bell-shaped curve, representing the standard normal distribution. The shaded area under the curve signifies the cumulative probability corresponding to the Z-score. **Table Explanation:** - The Z-scores range from -3.4 to -0.1 in increments of 0.1. - The table headers (0.00 to 0.09) represent the second decimal place of the Z-score. - For example, a Z-score of -2.5 with a second digit of 0.04 corresponds to a cumulative probability of 0.0062. **Standard Normal Distribution Table (Page 2)** This continuation of the standard normal distribution table covers positive Z-scores, providing the cumulative probability for each. **Diagram Explanation:** Similarly, a bell-shaped curve appears, indicating the cumulative probability area to the left of the specified Z-score. **Table Explanation:** - The Z-scores range from 0.0 to 2.9 in increments of 0.1. - The cumulative probabilities increase progressively since they represent areas under the curve as you move right on the Z-distribution. Together, these tables are essential for calculating probabilities and understanding the properties of the normal distribution in various statistical analyses.
Expert Solution
Step 1

Given,

mean (μ)  = 91 

standard deviation (σ) = 10

d) What effect does increasing the sample size has on its probability?

Answer :  Increasing the sample size decreases the probability because oX decreases as n increases.(option A)

 

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