Question

- A Study studied The birth weight of 2997 babies born in the United States. The main weight was 3234 grams with a standard deviation of 871 grams. Assume that birthweight data are approximately bell shaped. Estimate the number of newborns who weighed between 1492 grams in 4976 grams. Write only a number as your answer. Round your answer to the nearest whole number

- The GMAC insurance company reported that the mean score on the national drivers test was 81.4 with a standard deviation of 3.1 points. The test scores are approximately bell shaped. Approximately 68% of all test scores were between two values A & B. What is the value of a? Write only A number as your answer. Round to one Decimal Place.

Answer 1

Solution:- Given that mean = 3234, sd = 871

P(1492 < X < 4976) = P((1492-3234)/871 < (X-mean)/sd < (4976-3234)/871)
= P(-2 < Z < 2)
= 0.9545
  
=> The estimated number of newborns who weighed between 1492 and 4976 grams are 0.9544*2997 = 2860.3368 = 2860

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Solution:-

In mathematical notation, these facts can be expressed as follows, where x is an observation from a normally distributed random variable, μ is the mean of the distribution, and σ is its standard deviation:
P( μ – σ ≤ x ≤ μ + σ ) ≈ 0.68

=> So here A = μ – σ = 81.4 – 3.1 = 78.3