Question

1. The heights of kindergarten children are approximately normally distributed with a mean height of 39 inches and a standard deviation of 2 inches. A classroom of 20 of these children is used as a sample. What is the probability that the average height , for the class is greater than 40 inches? Illustrate with a graph.

ANSWER: 0.0127

2. The heights of kindergarten children are approximately normally distributed with a mean height of 39 inches and a standard deviation of 2 inches. If a first-time kindergarten teacher finds the average height for the 20 students in her class is 40.3 inches, would that be unusual? Explain.

ANSWER: 0.0018

3. A bottling company uses a filling machine to fill plastic bottles with a popular cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a normal distribution with mean µ = 298 ml and standard deviation σ =3.2 ml. What is the probability that the mean contents of all the bottles in a six-pack is less than 300 ml?

ANSWER: 0.9370

4. The price of an office visit at local area veterinary offices was found to have a mean of $27.50 and a standard deviation of $2.80. If the prices are assumed to be normally distributed, what is the probability that a randomly selected veterinarian:

charges more than $30 for an office visit

ANSWER: 0.1867

5. The time (in days) spent waiting for a heart transplant in California and Oregon for patients with type A+ blood can be found using a normal distribution with µ= 125 days, and = 20.5 days. Draw graphs and compute the following: what range of waiting times make up the middle 90% of waiting times for heart transplant in these state?

ANSWER: Lower: 91.2805

Upper: 158.7195

PLEASE SHOW WORK STEP BY STEP, Explanation and the technology/manual was to compute it

Answer 1

Question 1 :

Given mean = 39 inches

standard deviation = 2 inches.

Sample n =20

probability that the average height , for the class is greater than 40 inches

P( X > 40 ) =  x - μ/ σ / √n

= 40 - 39 / 2 /√20

= 2.236

P( Z > 2.236) =1−P ( Z<2.236 )=1−0.9875=0.0125

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