Question

the acceptable level for insect filth in a certain food item is 3 insect fragments (larvae, eggs, body parts, and so on) per 10 gram. a simple random sample of 50 ten-gram portions of the food item is obtained and results in a sample mean of x̄ = 3.2 insect fragments per ten-gram portion. complete parts (a) through (c) below.
click here to view the standard normal distribution table (page 1).
click here to view the standard normal distribution table (page 2).
(b) what is the mean and standard deviation of the sampling distribution of x̄ assuming μ = 3 and σ = √3?
μₓ̄ = 3 (round to three decimal places as needed.)
σₓ̄ = 0.245 (round to three decimal places as needed.)
(c) what is the probability a simple random sample of 50 ten-gram portions of the food item results in a mean of at least 3.2 insect fragments?
p(x̄ ≥ 3.2) = 0.2061 (round to four decimal places as needed.)
is this result unusual?
a. this result is unusual because its probability is large.
b. this result is unusual because its probability is small.
c. this result is not unusual because its probability is small.
d. this result is not unusual because its probability is large.
clear all

Explanation:

To determine if the result is unusual, we use the probability from part (c), \( P(\bar{x} \geq 3.2) = 0.2061 \). A result is considered unusual if its probability is less than 0.05 (a common threshold). Since \( 0.2061 > 0.05 \), the probability is large enough that the result is not unusual. Among the options, option C states "This result is not unusual because its probability is large," which matches our reasoning.

Answer:

C. This result is not unusual because its probability is large.