Questions: Suppose the birth weights of full-term babies are normally distributed with mean 3300 grams and standard deviation σ=525 grams. Complete parts (a) through (c) below.
(c) Suppose the area under the normal curve to the right of X=4350 is 0.0228. Provide an interpretation of this result. Select the correct choice below and fill in the answer box to complete your choice.
(Type a whole number.)
A. The probability is 0.0228 that the birth weight of a randomly chosen full-term baby in this population is less than grams.
B. The probability is 0.0228 that the birth weight of a randomly chosen full-term baby in this population is more than grams.
Transcript text: Suppose the birth weights of full-term babies are normally distributed with mean 3300 grams and standard deviation $\sigma=525$ grams. Complete parts (a) through (c) below.
(c) Suppose the area under the normal curve to the right of $\mathrm{X}=4350$ is 0.0228. Provide an interpretation of this result. Select the correct choice below and fill in the answer box to complete your choice.
(Type a whole number.)
A. The probability is 0.0228 that the birth weight of a randomly chosen full-term baby in this population is less than $\square$ grams.
B. The probability is 0.0228 that the birth weight of a randomly chosen full-term baby in this population is more than $\square$ grams.
Solution
Solution Steps
Step 1: Interpret the area under the curve
The area to the right of X = 4350 under the normal curve represents the probability that a randomly selected full-term baby weighs more than 4350 grams. This probability is given as 0.0228.
Step 2: Match the interpretation to the given options
Option B correctly states that the probability is 0.0228 that the birth weight of a randomly chosen full-term baby in this population is more than a certain number of grams. Option A incorrectly uses "less than".
Step 3: Identify the correct value for the blank
The value in question is 4350 grams.
Final Answer:
The correct choice is B, and the missing value is 4350. So, the complete sentence is: The probability is 0.0228 that the birth weight of a randomly chosen full-term baby in this population is more than $\boxed{4350}$ grams.