Suppose the numbers of a particular type of bacteria in samples of l millilitre (mL) of drinking water tend to be approximately normally distributed, with a mean of 84 and a standard deviation of 6. What is the probability that a given l-mL sample will contain more than 94 bacteria? (Round your answer to four decimal places.) :I 1. [14 Points] MENDSTATC4 6.E.035. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider a binomial random variable X with n = 25 and p = 0.6. (a) Can the normal approximation be used to approximate probabilities in this case' Why or why not? 0 Yes, the normal approximation to the binomial probabilities can always be used. 0 Yes, because rip and nq are greater than S. 0 Yes, because hp and Mg are greater than 100. O No, because rip and nq are less than 5. O No, because no and nq are less than 100. (b) What are the mean u and standard deviation 0 of X? (Round your answer for standard deviation to three decimal places.) (c) Using the correction for continuity, approximate F(X > 8). (Round your answer to four decimal places.) mew: LetX be a binomial random variable with n = 25 and p = 0.3. (a) Is the normal approximation appropriate for this binomial random variable? 0 Yes, the normal approximation to the binomial probabilities can always be used. 0 Yes, because hp and no are greaterthan 5. 0 Yes, because hp and no are greaterthan 100. O No, because rip and nq are less than 5. O No, because hp and nq are less than 100. (b) Find the mean ,u and standard deviation 0 for X. [Round your answer for standard deviation to three decimal places.) (c) Use the normal approximation to find P(7 S X S 8). (Round your answer to four decimal places.) W,: (d) Use the Cumulative Binomial Probabilities table to find the exact probability P(7 S X S 8). (Enter your answer to three decim W,: Compare the results of parts (c) and (d). How close was your approximation? 0 The difference between the probabilities in parts (c) and (cl) is less than 0.01. O The difference between the probabilities in parts (c) and (d) is between 0.01 and 0.1. O The difference between the probabilities in parts (c) and (d) is more than 0.1