1. Let X be a random variable that represents the weights inkilograms (kg) of a healthy adult female deer (doe) from Mesa VerdeNational Park. X has a distribution that is approximately normalwith µ = 63.0 kg and standard deviation σ = 7.1 kg. A doe isconsidered to be malnourished if it weighs less than 54 kg.
a. If the doe population is healthy, what is the probabilitythat a single doe captured weighs less than 54 kg?
b. What is the probability that the mean weight of a randomsample of 50 does is less than 54 kg?
c. Create a 95% confidence interval for the mean weight of arandom sample of 36 does in Mesa Verde National Park.
2. A CPA firm is auditing the accounts of a large interstatebanking system. Out of a random sample of 152 accounts, it wasfound that 19 had transaction errors. Let p be the number ofaccounts with transaction errors.
a. Find a point estimate for p ( pˆ ):
b. Find a 99% confidence interval for p: . An article in thelocal paper claims that the average amount spent in a visit to afast food restaurant is $20. Is the fast food restaurant in problem#1 unusually inexpensive? (In other words, are people spending lessat the local fast food restaurant than the population does at anaverage fast food restaurant?) Assuming that the amount peoplespend is normally distributed, conduct a hypothesis test using a 5%significance level. a. Ho: Ha: b. Is this a right-tailed,two-tailed or left-tailed test?
c. Compute the z or t test statistic. Show the correctcomputation.
d. Find the p-value for the test statistic. e. Based on youranswers above, do you reject or fail to reject the null hypothesis?What do you conclude about the average cost of this fast foodrestaurant?
