The overhead reach distances of adult females are normally distributed with a mean of 202.5 cm and a standard deviation

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The overhead reach distances of adult females are normally distributed with a mean of 202.5 cm and a standard deviation of 7.8 cm. a. Find the probability that an individual distance is greater than 215.00 cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 200.70 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? a. The probability is (Round to four decimal places as needed.) b. The probability is (Round to four decimal places as needed.)
c. Choose the correct answer below. O A. The normal distribution can be used because the mean is large. OB. The normal distribution can be used because the finite population correction factor is small. OC. The normal distribution can be used because the original population has a normal distribution. O D. The normal distribution can be used because the probability is less than 0.5
In a science fair project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily's hand without seeing it and without touching it. Among 325 trials, the touch therapists were correct 153 times. Complete parts (a) through (d). C a. Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses? (Type an integer or a decimal. Do not round.) b. Using Emily's sample results, what is the best point estimate of the therapists' success rate? (Round to three decimal places as needed.)
d. What do the results suggest about the ability of touch therapists to select the correct hand by sensing energy fields? OA. Since the lower confidence limit is below 0.5, there does not appear to be sufficient evidence that touch therapists can select the correct hand by sensing energy fields. B. Since the upper confidence limit is above 0.5, there appears to be evidence that touch therapists can select the correct hand by sensing energy fields. OC. Since the confidence interval is not entirely below 0.5, there appears to be evidence that touch therapists can select the correct hand by sensing energy fields. OD. Since the confidence interval is not entirely above 0.5, there does not appear to be sufficient evidence that touch therapists can select the correct hand by sensing energy fields