Problem 6 Suppose the weights of king salmon are normally distributed with a mea
ID: 3051700 • Letter: P
Question
Problem 6 Suppose the weights of king salmon are normally distributed with a mean of 35 pounds and a standard deviation of 4.25 pounds (refer to problem 2). (a) What is the probability that a king salmon weighs over 39 pounds? Would you be surprised if a king salmon you caught weighed 39 pounds? (b) Suppose on a day, 9 king salmon are caught. Describe the sampling distribution of sample mean. (c) What is the probability that the sample mean weight of 9 king salmon is over 39 pounds? Would you be surprised if 9 king salmon you caught had an average of 39 pounds?Explanation / Answer
Mean is 35 and standard deviation is 4.25
a) P(x>39)=P(z>(39-35)/4.25)=P(z>0.94)=1-P(z<0.94), from normal distribution table we get 1-0.8264=0.1736, no i would not be surprised because the probability is not very low
b) for 9 salmons, the mean is same as 35 and standard error is s=4.25/sqrt(9)=1.417
c) P(xbar>39)=P(z>(39-35)/1.417)=P(z>2.82) or 1-P(z<2.82) or 1-0.9976=0.0024, yes i would be surprised