Stats: Modeling the World Nasta Edition Grades 9-12
Stats: Modeling the World Nasta Edition Grades 9-12
3rd Edition
ISBN: 9780131359581
Author: David E. Bock, Paul F. Velleman, Richard D. De Veaux
Publisher: PEARSON
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Chapter 6, Problem 45E

a)

To determine

To find fraction of kindergarten kids should the company expect to be less than 3 feet tall.

a)

Expert Solution
Check Mark

Answer to Problem 45E

The 11.12% of kindergarten kids should the company expected to be less than 3 feet tall.

Explanation of Solution

Given:

  μ = 38.2

  σ = 1.8

  x =36

Using z-score,

  z=3638.21.8=1.22

  P(Z<1.22)=0.1112=11.12%

Hence, 11.12% of kindergarten kids should the company expected to be less than 3 feet tall.

b)

To determine

To find the percent of middle 80% of kindergarteners.

b)

Expert Solution
Check Mark

Answer to Problem 45E

The middle 80%of kindergarteners are expected to be between 35.896 and 40.504 inches.

Explanation of Solution

Given:

  μ = 38.2

  σ = 1.8

Middle 80% values mean we need to find z-scores corresponding to a probability of 0.1 or 0.9.

  P(-z

So, z = ±1.28

Therefore,

  x=38.2+(1.28)×1.8=35.896x=38.2+1.28×1.8=40.504

Hence, the middle 80% of kindergarteners are expected to be between 35.896 and 40.504 inches.

c)

To determine

To find the biggest 10% of kindergarteners.

c)

Expert Solution
Check Mark

Answer to Problem 45E

The biggest 10% of kindergarteners are expected to be more than 40.504 inches tall.

Explanation of Solution

Given:

  μ = 38.2

  σ = 1.8

The biggest 10% means z corresponding to probability of 90%

  P(Z< z) = 0.90

So, z = 1.28

Therefore,

  x=38.2+1.28×1.8=40.504

Hence, the biggest10% of kindergarteners are expected to be more than 40.504 inches tall.

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