A large pet store that specializes in tropical fish has several thousand guppies. The store claims that the guppies have a mean length of 5 cm and a standard deviation of 0.5 cm. Assume that the distribution of guppy length is normal. You come to the store and buy 10 randomly-selected guppies and find that the mean length of your 10 guppies is 4.8 cm. This makes you suspect that the mean fish length is not what the store says it is. Use the procedures from this chapter to decide whether the store is being honest or not. Please do all of your work on a separate piece of paper and submit a photo of your work. Make sure you include the following in your response:
a) A description of the center, shape, and spread of the sampling distribution for this statistic. All conditions need to be included.
b) Calculate the probability of getting a sample size of 4.8 cm or less. (show all work)
c) Explain your conclusions about the honesty of the store.