Questions: Elephants have the longest pregnancy of all mammals. Suppose that for Asian elephants, the lengths of pregnancies are normally distributed with a mean of 624 days and a standard deviation of 25 days. Use this table or the ALEKS calculator to find the percentage Asian elephant pregnancies that are shorter than 675 days. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23 % ).

Elephants have the longest pregnancy of all mammals. Suppose that for Asian elephants, the lengths of pregnancies are normally distributed with a mean of 624 days and a standard deviation of 25 days. Use this table or the ALEKS calculator to find the percentage Asian elephant pregnancies that are shorter than 675 days. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23 % ).
Transcript text: Elephants have the longest pregnancy of all mammals. Suppose that for Asian elephants, the lengths of pregnancies are normally distributed with a mean of 624 days and a standard deviation of 25 days. Use this table or the ALEKS calculator to find the percentage Asian elephant pregnancies that are shorter than 675 days. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example $98.23 \%$ ).
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Solution

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Solution Steps

Step 1: Define the Normal Distribution Parameters

For Asian elephants, the lengths of pregnancies are normally distributed with the following parameters:

  • Mean (\(\mu\)) = 624 days
  • Standard Deviation (\(\sigma\)) = 25 days
Step 2: Calculate the Cumulative Distribution Function (CDF)

We want to find the probability that a pregnancy is shorter than 675 days, which can be expressed as: \[ P(X \leq 675) \] Using the CDF of the normal distribution, we find: \[ P(X \leq 675) \approx 0.9793 \]

Step 3: Convert to Percentage

To express this probability as a percentage, we multiply by 100: \[ \text{Percentage} = 0.9793 \times 100 = 97.93\% \]

Final Answer

The percentage of Asian elephant pregnancies that are shorter than 675 days is \\(\boxed{97.93\%}\\).

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