SOLUTION: The table below describes results from random selection of eight live births from eight different sets of parents. The random variable x represents the number of girls among the ei

Question 1192121: The table below describes results from random selection of eight live births from eight different sets of parents. The random variable x represents the number of girls among the eight live births. Is 6 a significantly high number of girls out of 8 live births?

Probability Distribution of Girls in x Live Births
x P(x)
0 0.004
1 0.008
2 0.104
3 0.251
4 0.266
5 0.251
6 0.104
7 0.008
8 0.004

Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's how to determine if 6 girls out of 8 live births is significantly high:
1. **Calculate the Mean (μ):**
μ = Σ [x * P(x)]
μ = (0 * 0.004) + (1 * 0.008) + (2 * 0.104) + (3 * 0.251) + (4 * 0.266) + (5 * 0.251) + (6 * 0.104) + (7 * 0.008) + (8 * 0.004)
μ = 4
2. **Calculate the Standard Deviation (σ):**
σ = sqrt( Σ [(x - μ)² * P(x)] )
σ = sqrt( (0-4)² * 0.004 + (1-4)² * 0.008 + (2-4)² * 0.104 + (3-4)² * 0.251 + (4-4)² * 0.266 + (5-4)² * 0.251 + (6-4)² * 0.104 + (7-4)² * 0.008 + (8-4)² * 0.004 )
σ ≈ 1.27
3. **Calculate the Range of Usual Values (using the Range Rule of Thumb):**
* Lower Bound: μ - 2σ = 4 - 2 * 1.27 ≈ 1.46
* Upper Bound: μ + 2σ = 4 + 2 * 1.27 ≈ 6.54
4. **Compare the Observed Value:**
The observed value is 6 girls.
5. **Make a Decision:**
Since 6 falls within the range of usual values (1.46 to 6.54), it is *not* considered significantly high.
**Conclusion:**
6 girls out of 8 live births is within the expected range based on the given probability distribution. Therefore, it is not considered a significantly high number.

RELATED QUESTIONS
Eight winners for a door prize will be selected at random, without replacement, from a... (answered by stanbon)

Find the probability of exactly eight boys in ten... (answered by edjones)

Suppose a neighbourhood is particularly diverse in terms of the ethnic origin of its... (answered by stanbon)

A 0.1 significance level is used for a hypothesis test of the claim that when parents use (answered by stanbon)

A committee consisting of 6 people is to be selected from eight parents and four... (answered by stanbon)

A committee of five people must be selected from five men and eight women. How many... (answered by stanbon)

how long does it take to commute from work to home. it depends on several factors,... (answered by stanbon)

Below are two sets of data. One of the sets describes a linear function and the other... (answered by stanbon,Fombitz,vleith)

A parent- teacher committee consisting of 4 people is to be formed from 20 parents and 5... (answered by solver91311)