Question

Using the mean and the standard deviation you found in the second question​ (rounded to four​ decimals), answer the following probability questions using​ Stat>Calculators>Normal.

For​ each, copy and paste the StatCrunch output in the SHOW YOUR WORK.

Here is a short video that shows how to insert multiple graphs into the SHOW WORK​ area:

SHOW WORK

1. What is the probability that a randomly selected​ 5-year-old female will be taller than 40 inches​ tall? (Round to 4 decimal​ places)  nothing

2. What is the probability that a randomly selected​ 5-year-old female will be shorter than 35 inches​ tall? (Round to 4 decimal​ places) nothing

3. What is the probability that a randomly selected​ 5-year-old female will be between 39 and 47 inches​ tall? ​ (Round to 4 decimal​ places) nothing

Question 2

Here is the data​ again: 44.5 42.4 42.2 46.2 45.7 44.8 43.3 39.5 45.4 43.0 43.4 44.7 38.6 41.6 50.2 46.9 39.6 44.7 36.5 42.7 40.6 47.5 48.4 37.5 45.5 43.3 41.2 40.5 44.4 42.6 42.0 40.3 42.0 42.2 38.5 43.6 40.6 45.0 40.7 36.3 44.5 37.6 42.2 40.3 48.5 41.6 41.7 38.9 39.5 43.6 41.3 38.8 41.9 40.3 42.1 41.9 42.3 44.6 40.5 37.4 44.5 40.7 38.2 42.6 44.0 35.9 43.7 48.1 38.7 46.0 43.4 44.6 37.7 34.6 42.4 42.7 47.0 42.8 39.9 42.3

What is the​ mean 42.2238

What is the standard​ deviation? (Round to 4 decimal​ places) s​ = 3.1310

Answer 1

Solution:-

1) The probability that a randomly selected​ 5-year-old female will be taller than 40 inches​ tall is 0.2388.

x = 40

By applying normal distribution:-

z = 0.7103

P(z > 0.7103) = 0.2388

2) The probability that a randomly selected​ 5-year-old female will be shorter than 35 inches​ tall is 0.0104.

x = 35

By applying normal distribution:-

z = - 2.31

P(z < - 2.31) = 0.0104

3) The probability that a randomly selected​ 5-year-old female will be between 39 and 47 inches​ tall is 0.7855.

x₁ = 39

x₂ = 47

By applying normal distribution:-

z₁ = - 1.03

z₂ = 1.53

P( -1.03 < z < 1.53) = P(z > - 1.03) - P(z > 1.53)

P( -1.03 < z < 1.53) = 0.8485 - 0.0630

P( -1.03 < z < 1.53) = 0.7855