A large tank of fish from a hatchery is being delivered to a lake. The hatchery...

A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 5inches. A random sample of 47 fish is taken from the tank. Let x be the mean sample length of these fish. What is the probability that x is within 0.5 inch of the claimed population mean? (Round your answer to four decimal places.)

Solutions

Expert Solution

Solution :

Given that,

mean = = 15

standard deviation = = 5

n = 47

= = 15

= / n = 5/47 = 0.7293

P( 14.5 < < 15.5) = P((14.5 - 15) / 0.7293 < ( - ) / < (15.5 - 15) / 0.7293))

= P(-0.69 < Z < 0.69)

= P(Z < 69) - P(Z < -0.69) Using z table,

= 0.7549 - 0.2451

= 0.5098

The probability that x is within 0.5 inch of the claimed population mean is 0.5098.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A large tank of fish from a hatchery is being delivered to a lake. The hatchery...

A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 6 inches. A random sample of 60 fish is taken from the tank. Let x be the mean sample length of these fish. What is the probability that x is within 0.5 inch of the claimed population mean? a. .5000 b. .4814 c. .1467 d. .0325

A large tank of fish from a hatchery is being delivered to a lake. The hatchery...

A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 3 inches. A random sample of 20 fish is taken from the tank. Let x be the mean sample length of these fish. What is the probability that x is within 0.5 inch of the claimed population mean? (Round your answer to four decimal places.)

A large tank of fish from a hatchery is being delivered to a lake. The hatchery...

A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 4 inches. A random sample of 28 fish is taken from the tank. Let x be the mean sample length of these fish. What is the probability that x is within 0.5 inch of the claimed population mean? (Round your answer to four decimal places.)

A large population of fish live in a lake. The color of their scales is determined...

A large population of fish live in a lake. The color of their scales is determined by two different alleles of the S gene, S1 and S2. Homozygous S1 fish have yellow scales, S2 homozygotes have blue scales, and heterozygotes are green. Scientists catch 100 fish at random and record their colors. Among those 100 fish are 30 yellow, 50 blue, and 20 green ones. After the original sample is analyzed, an asteroid landed in the lake and killed all...

There is a small lake in the rain forest that is home of large fish stocks....

There is a small lake in the rain forest that is home of large fish stocks. Only one tribe has access to that. Explain the determiation of optimal level of catch. Would there be a difference if all of the tribes had an access to that? Explain your answer. Could this situation be resolved through property rights and a Coasian bargaining process? Explain your answer.

1. A scientist collects fish from two lakes. The first lake is known to have large...

1. A scientist collects fish from two lakes. The first lake is known to have large fish and the second is known to have small fish. The fish caught from the first lake have weights, in grams, of: c(41.4, 35.9, 35.7, 29.9, 48.3, 36.7, 37.2, 29.7, 45.5) and fish caught from the second lake has weights of: c(41.9, 35.4, 35.4, 23.9, 34.4, 39.9, 34.2, 42.3) Is there evidence that the first group is actually more active than the second? （Pls...

Fish weights: A fish hatchery raises trout to stock streams and lakes. The weights, in ounces,...

Fish weights: A fish hatchery raises trout to stock streams and lakes. The weights, in ounces, of a sample of 18 trout at their time of release are as follows. 9.9 11.3 11.4 9.0 10.1 8.2 8.9 9.9 10.5 8.6 7.8 10.8 8.4 9.6 9.9 8.4 9.0 9.1 Construct a stem-and-leaf plot for this sample. Is it reasonable to treat the sample as coming from an approximately normal population? Explain. Include support for your decision. Graphical displays should be formatted...

Hester’s Hatchery raises fish. At the end of the current season she has 2,100 fish in...

Hester’s Hatchery raises fish. At the end of the current season she has 2,100 fish in the hatchery. She can harvest any number of fish that she wishes, selling them to restaurants for $5 a piece. Because big fish make little fish, for every fish that she leaves in the hatchery this year, she will have two fish at the end of next year. The price of fish is expected to be $5 each next year as well. Hester relies...

A fish hatchery manager estimates that on average fisherpersons catch 3.5 fish each fishing trip. A...

A fish hatchery manager estimates that on average fisherpersons catch 3.5 fish each fishing trip. A random sample of 10 fisherpersons showed they caught 3.9 fish per trip, with a standard deviation of 1.7 fish. Perform a test of hypothesis at a .10 alpha level to determine whether or not her claim is true. Use a two tailed test of hypothesis

Subjects