Estimate the probability of getting exactly 43 boys in 90 births. estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. round to four decimal places.

The probability of getting exactly 43 boys is given by:
P(X = 43) = P(X ≤ 43) - P(X ≤ 42)

First, let's find P(X ≤ 43). We know n = 90 and the probability of getting a boy is p = 0.50
Calculate the mean: μ = n · p = 90 · 0.5 = 45
Calculate the standard deviation: σ = √[n · p · (1 - p)] = √(90 · 0.5 · 0.5) = 4.743
Calcuate the z-score: z = (X - μ) / σ = (43 - 45) / 4.743 = -0.42
Now, look at a z-score table in order to find to what probability this value corresponds: P(z ≤ -0.42) = 0.3372 = P(X ≤ 43)

Now, repeat the calculations for X = 42: 
μ and  σ stay the same,
z = (X - μ) / σ = (42 - 45) / 4.743 = -0.63
P(z ≤ -0.63) = 0.2643 = P(X ≤ 42)

Now, find the difference:
P(X = 43) = P(X ≤ 43) - P(X ≤ 42) = 0.3372 - 0.2643 = 0.0729

You have around 7.3% of probability to get exactly 43 boys in 90 births.

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