Answered: The incubation time for Rhode Island…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 2CYU

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Question

The incubation time for Rhode Island Red chicks is normally distributed with mean of 30 days and standard deviation of approximately 2 days. If 1000 eggs are being incubated, how many chicks do we expect will hatch in 24 to 26 days?

Group of answer choices

21 chicks

819 chicks

136 chicks

341 chicks

157 chicks

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

Let X be the incubation time for the chicks.

It is given,

$X ~ N (30, 2^{2})$

To calculate P[24<X<26]

This is calculated using CLT.

$P [24 < X < 26] = P [\frac{24 - 30}{2} < \frac{X - 30}{2} < \frac{26 - 30}{2}] = P [- 3 < Z < - 2] = ϕ (- 2) - ϕ (- 3) T h e v a l u e s a r e o b t a i n e d f r o m s \tan d a r d n o r m a l t a b l e s . T h e r e f o r e, P [24 < X < 26] = 0.02275 - 0.00135 = 0.0214 .$

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