help me please
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). (a) What is the probability a randomly selected student in the city will read more than 96 words per minute? The probability is. (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 less than 96 words per minute. B. If 100 different students were chosen from this population, we would expect to read more than 96 words per minute. O C. If 100 different students were chosen from this population, we would expect to read exactly 96 words per minute. (b) 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 96 words per minute? The probability is. (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 independent samples of n = 10 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of less than 96 words per minute. B. If 100 independent samples of n = 10 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of more than 96 words per minute. C. If 100 independent samples of n = 10 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of exactly 96 words per minute. (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 96 words per minute? The probability is. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. O A. If 100 independent samples of n = 20 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of more than 96 words per minute. O B. If 100 independent samples of n = 20 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of less than 96 words per minute. C. If 100 independent samples of n = 20 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of exactly 96 words per minute. (d) What effect does increasing the sample size have on the probability? Provide an explanation for this result.(d) What effect does increasing the sample size have on the probability? Provide an explanation for this result. O A. Increasing the sample size increases the probability because o- decreases as n increases. O B. Increasing the sample size increases the probability because o increases as n increases. O C. Increasing the sample size decreases the probability because of decreases as n increases. O D. Increasing the sample size decreases the probability because of increases 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 18 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.) O A. A mean reading rate of 93.8 wom 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 = 18 students. The new program is not abundantly more effective than the old program. J 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 n = 18 students. The new program is abundantly more effective than the old program. (f) There is a 5% chance that the mean reading speed of a random sample of 20 second grade students will exceed what value? There is a 5% chance that the mean reading speed of a random sample of 20 second grade students will exceed wpm. (Round to two decimal places as needed.)
