A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 49 0 and 54 0 minutes Find the probability that a given class period runs between 51,5 and 51 75 minutes. Find the probability of selecting a class that runs between 51 5 and 5175 minutes, (Round to three decimal places as needed.) Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Click to view page 1 of the table. Click to view page 2 of the table. 0.9842 N+ The indicated z score is. (Round to two decimal places as needed.)Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. Click to view page 1 of the table. Click to view page 2 of the table. 75 The area of the shaded region is . (Round to four decimal places as needed.)Assume that females have pulse rates that are normally distributed With a mean of p : 73 0 beats per minute and a standard deviation of u :12 5 beats per minute Complete parts (a) through to) below a. lfl adult female is randomly selected, find the probability that her pulse rate is less than 77 beats per minute The probability is . (Round to four decimal places as needed.) b. It 25 adult females are randomly selected, find the probability that they have pulse rates With a mean less than 7? beats per minute. The probability is . (Round to four decimal places as needed) 1:. Why can the normal distribution be used in part (b) even though the sample size does not exceed 30'? . Since the dis ribution is of indiwduals. not sample means' the distribution is a normal distribution for any sample size . Since the mean pulse rate exceeds 30. the distribution of sample means is a normal distribution for any sample SlZe. . Since the dis ribution is of sample means, not individuals the distribution is a normal distribution for any sample size {I D. Since the original population has a normal distribution the distribution of sample means is a normal distribution for any sample size. 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 293 trials, the touch therapists were correct 1 times. Complete parts (a) through (d). 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.) c. Using Emily's sample results, construct a 95% confidence interval estimate of the proportion of correct responses made by touch therapists.