19- ### Analysis of Reading Speeds in Second Grade Students#### Overview:The reading speed of second-grade students in a large city follows a normal distribution. The mean reading speed is 89 words per minute (wpm), and the standard deviation is 10 wpm. This study involves evaluating the probabilities associated with different sample sizes and reading speeds.#### Part (a):For samples of \( n = 10 \) students:- **Option A**: If 100 independent samples were chosen from this population, we would expect \([blank]\) sample(s) to have a sample mean reading rate of exactly 95 words per minute.- **Option B**: If 100 independent samples were chosen from this population, we would expect \([blank]\) sample(s) to have a sample mean reading rate of less than 95 words per minute.- **Option C**: If 100 independent samples were chosen from this population, we would expect \([blank]\) sample(s) to have a sample mean reading rate of more than 95 words per minute.#### Part (c):What is the probability that a random sample of 20 second-grade students from the city results in a mean reading rate of more than 95 words per minute?- **The probability is \([blank]\)** - (Round to four decimal places as needed.)#### Interpretation of Probability:Select the correct choice and complete the statement:- **Option A**: If 100 independent samples of \( n = 20 \) students were chosen from this population, we would expect \([blank]\) sample(s) to have a sample mean reading rate of more than 95 words per minute.- **Option B**: If 100 independent samples of \( n = 20 \) students were chosen from this population, we would expect \([blank]\) sample(s) to have a sample mean reading rate of exactly 95 words per minute.- **Option C**: If 100 independent samples of \( n = 20 \) students were chosen from this population, we would expect \([blank]\) sample(s) to have a sample mean reading rate of less than 95 words per minute.#### Instructions:- Fill in the blanks with the appropriate numbers based on statistical calculations.- Interpret the probability by selecting the most accurate statement. Understanding these probabilities can offer insights into the distribution and variance of reading speeds within this population. **Reading Speed Analysis of Second Grade Students**The reading speed of second grade students in a large city is analyzed here, assuming an approximately normal distribution. The mean reading speed is 89 words per minute (wpm) with a standard deviation of 10 wpm.**(a) Probability of Reading More Than 95 Words Per Minute**- **Question:** What is the probability that a randomly selected student in the city will read more than 95 words per minute?- **Answer Box:** The probability is \_\_\_. (Round to four decimal places as needed.)- **Interpretation Choices:** - **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.**(b) Probability of a Sample Mean Exceeding 95 Words Per Minute**- **Question:** What is the probability that a random sample of 10 second grade students from the city results in a mean reading rate of more than 95 words per minute?- **Answer Box:** The probability is \_\_\_. (Round to four decimal places as needed.)This exercise delves into calculating probabilities using normal distribution principles, an essential skill in statistics.

Let X denote the reading speed of second grade students. Given that X follows N(mean = 89, SD = 10), then Z = (X - mean)/SD follows N(0,1)Interpretation of probabilities calculated above are a) The interpretation of probability = 0.2742 is C. If 100 different students were chosen from this population, we would expect 100× 0.2742 = 27.42 ≈ 27 to read more than 95 words per minute. b) The interpretation of probability = 0.0287 is C. If 100 independent samples of n = 10 students were chosen from this population, we would expect 100×0.0287 = 2.87 ≈ 3 sample(s) to have a sample mean reading rate of more than 95 words per minute. c) The interpretation of probability = 0.0037 is C. If 100 independent samples of n = 10 students were chosen from this population, we would expect 100×0.0037 = 0.37 = 0 sample(s) to have a sample mean reading rate of more than 95 words per minute.