   # Medical Science A medical research team has determined that for a group of 500 females, the length of pregnancy from conception to birth varies according to an approximately normal distribution with a mean of 266 days and a standard deviation of 16 days. (a) Use a graphing utility to graph the distribution. (b) Use a symbolic integration utility to approximate the probability that a pregnancy will last from 240 days to 280 days. (c) Use a symbolic integration utility to approximate the probability that a pregnancy will last more than 280 days. ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 9.3, Problem 55E
Textbook Problem
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## Medical Science A medical research team has determined that for a group of 500 females, the length of pregnancy from conception to birth varies according to an approximately normal distribution with a mean of 266 days and a standard deviation of 16 days.(a) Use a graphing utility to graph the distribution.(b) Use a symbolic integration utility to approximate the probability that a pregnancy will last from 240 days to 280 days.(c) Use a symbolic integration utility to approximate the probability that a pregnancy will last more than 280 days.

(a)

To determine

To graph: The distribution with the help of graphing utility. If in a medical research the team has found that for a group of 500 females the period for pregnancy from conception to birth varies according to the mean of 266 days and standard deviation of 16 days (assume the normal distribution taken place).

### Explanation of Solution

Given information:

In a medical research the team has found that for a group of 500 females the period for pregnancy from conception to birth varies according to the mean of 266 days and standard deviation of 16 days (assume the normal distribution taken place).

Graph:

Consider the provided probability density function,

f(x)=1σ2πe(xμ)22σ2, <x<

From the provided information the value of the mean is μ=266 days, the value of standard deviation σ=16 days.

Now, substitute the values of mean μ=266 days, standard deviation σ=16 days in the above formula as,

f(x)=1162πe(x266)22(16)2=1162πe(x266)22(256)=140

(b)

To determine

To calculate: The approximate probability that the pregnancy of women last from 240 days to 280 days. If in a medical research the team has found that for a group of 500 females the period for pregnancy from conception to birth varies according to the mean of 266 days and standard deviation of 16 days (assume the normal distribution taken place).

(c)

To determine

To calculate: The approximate probability that the pregnancy of women last more than, 280 days. If in a medical research the team has found that for a group of 500 females the period for pregnancy from conception to birth varies according to the mean of 266 days and standard deviation of 16 days (assume the normal distribution taken place).

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