Questions: The reading speed of second grade students in a large city is approximately normal, with a mean of 89 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). (a) What is the probability a randomly selected student in the city will read more than 95 words per minute? The probability is 0.2743. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. A. If 100 different students were chosen from this population, we would expect to read exactly 95 words per minute. B. If 100 different students were chosen from this population, we would expect to read less than 95 words per minute. C. If 100 different students were chosen from this population, we would expect to read more than 95 words per minute.

The reading speed of second grade students in a large city is approximately normal, with a mean of 89 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). (a) What is the probability a randomly selected student in the city will read more than 95 words per minute? The probability is 0.2743. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. A. If 100 different students were chosen from this population, we would expect to read exactly 95 words per minute. B. If 100 different students were chosen from this population, we would expect to read less than 95 words per minute. C. If 100 different students were chosen from this population, we would expect to read more than 95 words per minute.
Transcript text: The reading speed of second grade students in a large city is approximately normal, with a mean of 89 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). (a) What is the probability a randomly selected student in the city will read more than 95 words per minute? The probability is 0.2743 . (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. A. If 100 different students were chosen from this population, we would expect $\square$ to read exactly 95 words per minute. B. If 100 different students were chosen from this population, we would expect $\square$ to read less than 95 words per minute. C. If 100 different students were chosen from this population, we would expect $\square$ to read more than 95 words per minute.
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Solution

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Solution Steps

Step 1: Calculate the Z-Score

To find the probability that a randomly selected student reads more than 95 words per minute (wpm), we first calculate the Z-score for \( X = 95 \) wpm using the formula:

\[ Z = \frac{X - \mu}{\sigma} \]

Substituting the values:

\[ Z = \frac{95 - 89}{10} = \frac{6}{10} = 0.6 \]

Step 2: Find the Probability

Next, we use the Z-score to find the probability \( P(X > 95) \). This can be expressed as:

\[ P(X > 95) = 1 - P(X \leq 95) = 1 - \Phi(Z) \]

Using the standard normal distribution table, we find:

\[ P(X \leq 95) = \Phi(0.6) \approx 0.7257 \]

Thus, the probability of reading more than 95 wpm is:

\[ P(X > 95) = 1 - 0.7257 = 0.2743 \]

Step 3: Interpretation of the Probability

The probability \( P(X > 95) = 0.2743 \) indicates that if 100 different students were chosen from this population, we would expect:

\[ 0.2743 \times 100 \approx 27.43 \]

Rounding this to the nearest whole number, we expect approximately 27 students to read more than 95 wpm.

Final Answer

The probability that a randomly selected student reads more than 95 words per minute is \( 0.2743 \), and if 100 different students were chosen from this population, we would expect \( \boxed{27} \) to read more than 95 words per minute.

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