The heights of children 2 years old are normally distributed with a mean of 32 i

Question

The heights of children 2 years old are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches. Pediatricians regularly measure the heights of toddlers to determine whether there is a problem. There may be a problem when a child is in the top or bottom 5% of heights. Find the probability of these events.

a. A 2-year-old child is taller than 36 inches.
(to 4 decimals)

b. A 2-year-old child is shorter than 34 inches.
(to 4 decimals)

c. A 2-year-old child is between 30 and 33 inches tall.
(to 4 decimals)

Explanation / Answer

a) P(X > 36) = P(Z > (36-32) / 1.5) = P(Z >2.67) = 1-0.9962 = 0.0038

b ) P(X <34) = P(Z < (34-32) / 1.5) = P(Z <1.33) = 0.9088

c ) P(30 < X <33) = P(-1.33 < Z < 0.67) = 0.6563

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.