Suppose medical records indicate that

the length of newborn babies (in

inches) is normally distributed with a

mean of 20 and a standard deviation of

2.6. Find the probability that a given

infant is between 14.8 and 25.2 inches

long.

Step-by-step explanation:

Let x be the random variable representing the the length of newborn babies (in inches). Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 20 inches

σ = 2.6 inches

the probability that a given infant is between 14.8 and 25.2 inches long is expressed as

P(14.8 ≤ x ≤ 25.2)

For x = 14.8,

z = (14.8 - 20)/2.6 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.023

For x = 25.2

z = (25.2 - 20)/2.6 = 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.98

Therefore,

P(14.8 ≤ x ≤ 25.2) = 0.98 - 0.23 = 0.75

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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