Question

the weights of the largemouth bass in one location are skewed right with a mean of 5.17 pounds and a standard deviation of 4.13 pounds. an angler looks at the weights of a sample of 75 randomly selected largemouth bass that she has caught in this location.

use the normal distribution tool to answer the following.

(a) use a normal distribution approximation to find the probability that her sample will have a mean weight of 6 pounds or more.

(p(\bar{x} \ge 6) =)

(b) use a normal distribution approximation to find the probability her sample will have a mean weight less than 4.7.

(p(\bar{x} < 4.7) =)

enter your answers as a decimal to 4 decimal places or as a percentage including the % symbol.

Explanation:

Identify the sampling distribution parameters

Using the Sampling Distribution of the Mean and Standard Error of the Mean knowledge points

$$
LATEXBLOCK0
$$

Verify the Central Limit Theorem

Using the Central Limit Theorem knowledge point

$$
LATEXBLOCK1
$$

Calculate the probability for part (a)

Using the Normal Distribution Probability knowledge point

$$
LATEXBLOCK2
$$

Calculate the probability for part (b)

Using the Normal Distribution Probability knowledge point

$$
LATEXBLOCK3
$$

Answer:

Question 1

\(P(\bar{x} \ge 6) =\) <blank>0.0409</blank>

Question 2

\(P(\bar{x} < 4.7) =\) <blank>0.1622</blank>