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Chapter 3: Q 36. (page 175)

Fruit fly thorax lengths (2.2) Fruit flies are used frequently in genetic research because of their quick reproductive cycle. The length of the thorax (in millimeters) for male fruit flies is approximately Normally distributed with a mean of 0.80 mm and a standard deviation of 0.08 mm.21

a. What proportion of male fruit flies have a thorax length greater than 1 mm?

b. What is the 30th percentile for male fruit fly thorax lengths?

Short Answer

Expert verified

Part (a) The probability is0.0062

Part (b) The percentile is0.758

Step by step solution

01

Part (a) Step 1: Given information

Population mean (μ)=0.80

Standard deviation (σ)=0.08

02

Part (a) Step 2: Concept

The formula used:z=x−μσ

03

Part (a) Step 3: Calculation

The proportion of male fruit flies that are having thorax length above 1mmcan be calculated as:

P(x>1)=P(x−μσ>1−μσ)=P(Z>1−0.800.08)=P(Z>2.50)=0.0062

Therefore, the required proportion is0.0062

04

Part (b) Step 1: Explanation

From standard normal table, the z-value at 0.30 probability is -0.5244

The 30thpercentile can be calculated as:

x=μ+z×σ=0.80+(−0.5244)×0.08=0.758

Thus, the required percentile is 0.758

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