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Answer:
1. 15.87%
2. 6 pounds and 8.8 pounds.
3. 2.28%
4. 50% of newborn babies weigh more than 7.4 pounds.
5. 84%
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 7.4 pounds
Standard Deviation, σ = 0.7 pounds
We are given that the distribution of weights for newborn babies is a bell shaped distribution that is a normal distribution.
Formula:
1.Percent of newborn babies weigh more than 8.1 pounds
P(x > 8.1)
Calculation the value from standard normal z table, we have,
15.87% of newborn babies weigh more than 8.1 pounds.
2.The middle 95% of newborn babies weight
Empirical Formula:
- Almost all the data lies within three standard deviation from the mean for a normally distributed data.
- About 68% of data lies within one standard deviation from the mean.
- About 95% of data lies within two standard deviations of the mean.
- About 99.7% of data lies within three standard deviation of the mean.
Thus, from empirical formula 95% of newborn babies will lie between
95% of newborn babies will lie between 6 pounds and 8.8 pounds.
3. Percent of newborn babies weigh less than 6 pounds
P(x < 6)
Calculation the value from standard normal z table, we have,
2.28% of newborn babies weigh less than 6 pounds.
4. 50% of newborn babies weigh more than pounds.
The normal distribution is symmetrical about mean. That is the mean value divide the data in exactly two parts.
Thus, approximately 50% of newborn babies weigh more than 7.4 pounds.
5. Percent of newborn babies weigh between 6.7 and 9.5 pounds
84% of newborn babies weigh between 6.7 and 9.5 pounds.