Fishermen are visiting Irkutsk\'s Lake Baikal for the first time. There are many
ID: 3356875 • Letter: F
Question
Fishermen are visiting Irkutsk's Lake Baikal for the first time. There are many varieties of fish in Lake Baikal, but the tastiest is called the omul. A local guide takes them out to the beautiful lake and they drop in their lines. The guide tells them that she has fished there for 40 years, and caught literally thousands of omul. She says that the size of an omul today is Normally distributed with a mean of 50 cm and a standard deviation of 15 cm.
a) If what the guide says is true, what is the mean of the sampling distribution for a sample of 25 fish? Answer with the number of centimeters.
b) If what the guide says is true, what is the standard deviation of the sampling distribution for a sample of 25 fish? Answer with the number of centimeters. Be accurate to the nearest tenth.
c) Using what the guide says, construct a 99% confidence interval for samples of 25 fish. Enter the LOWER end of the confidence interval here. Be accurate to the nearest hundredth.
d) All morning the fishermen catch omul one after another, but they are getting a little suspicious of their guide. Their first 25 fish average 35 cm in length.Compared to your 99% confidence interval for samples of 25 fish, the fishermen's catch so far today is: groovy regardless of the confidence interval, below the confidence interval, above the confidence inteval or inside the confidence interval? Choose one.
Explanation / Answer
a) mean of the sampling distribution for a sample of 25 fish =50
b) standard deviation of the sampling distribution for a sample of 25 fish =std deviaiton/(n)1/2 =15/(25)1/2 =3
c)
for 99% Ci ; critical z =2.5758
hence LOWER end of the confidence interval =sample mean -z*std error =42.2725
d)
below the confidence interval
please revert for any clariifcaiton required
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