5. A certain strain of bacteria occurs in all ratttr milk. Let x be milliliter of milk {mL}. The health department has found that tithe milk is not contaminated then x has a distribution that is more or less mound-shaped and symmetrical. The mean of thex distribution is a = 3333. and the standard deviation is o= too. In a large commercial dairy. the health inspector takes 52 random samples of the milk produced each day. At the end of the day. the bacteria count in each of the 52 samples is averaged to obtain the sample mean bacteria count 2?. Assuming the milk is not contaminated. What is the probability that the average bacteria count for one day.r is batsmen 2453 and EEG bacteria per milliliter? {B} 6. Julia enjoys jogging. She has been jogging over a period of several years, during which time her physical condition has remained constantly good. Usually, she jogs 2 miles per day. The standard deviation of her times is o= 1.90 minutes. During the past year, Julia has recorded her times to run 2 miles. She has a random sample of 90 of these times. For these 90 times, the mean was x = 16.60 minutes. Let # be the mean jogging time for the entire distribution of Julia's 2-mile running times (taken over the past year). Find a 0.95 confidence interval for /. (8)7. For each of the following, state the null hypothesis: (4) a) A team of basketball players has a mean play time of 4.26 minutes per person. The coach hopes that introducing a new sports energy drink at halftime will allow the players to increase how long they are in the game. b) A group of farmers claim that the mean number of lake trout previously recorded in a lake is 55 fish/km, and that fertilizer run off is not negatively impacting the fish.8. Berick is an aging herding dog in Ontario who gets regular checkups from her owner, the local veterinarian. Let x be a random variable that represents Berick's resting heart rate (in beats per minute). From past experience, the vet knows that x has a normal distribution with o = 13. The vet checked the Sunny Veterinary Manual and found that for dogs of this breed # = 119, beats per minute. Over the past six weeks, Berick's heart rate (beats/min) measured: 93 111 110 88 118 112 The sample mean is x = 108.0. The vet is concerned that Berick's heart rate may be slowing. a) State the null hypothesis. (4) b) Does the data support the hypothesis that Berick's heart rate is slowing? (8)