1.A widget manufacturer knows that their widget lengths are approximately Normally distributed with mean 11.7 inches and standard deviation 2.1 inches.

One widget is 6.5 inches long. That widgetz-score is about...

. Round to 4 decimal places.

2.Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 564 and standard deviation 90.

Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 23.5 and standard deviation 3.2.

1. What is Elanor's standardized score?

a.

Round to 2 decimal places.

b. What is Gerald's standardized score?

Round to 2 decimal places.

3.Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0C and a standard deviation of 1.00C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between -2.626C and -2.381C.

P

(

2.626

<

Z

<

2.381

)

4.Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0C and a standard deviation of 1.00C. A single thermometer is randomly selected and tested. FindP₇, the 7-percentile. This is the temperature reading separating the bottom 7% from the top 93%.

P₇=C

5.A distribution of values is normal with a mean of 125.4 and a standard deviation of 28.3.

Find the probability that a randomly selected value is less than 204.6.

P(X< 204.6) =

answer as a number accurate to 4 decimal places. Answers obtained using exactz-scores orz-scores rounded to 3 decimal places are accepted.

6.A distribution of values is normal with a mean of 15.5 and a standard deviation of 22.1.

Find the probability that a randomly selected value is between 39.8 and 48.7.

P(39.8 <X< 48.7) =

answer as a number accurate to 4 decimal places. Answers obtained using exactz-scores orz-scores rounded to 3 decimal places are accepted.

7.A distribution of values is normal with a mean of 137.7 and a standard deviation of 8.8.

FindP₃₂, which is the score separating the bottom 32% from the top 68%.

P₃₂=

answer as a number accurate to 1 decimal place. Answers obtained using exactz-scores orz-scores rounded to 3 decimal places are accepted.

8.A particular fruit's weights are normally distributed, with a mean of 555 grams and a standard deviation of 21 grams.

If you pick one fruit at random, what is the probability that it will weigh between 529 grams and 576 grams

9.The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 32 liters, and standard deviation of 8.5 liters.

A) What is the probability that daily production islessthan 9.3 liters? Use technology (not tables) to get your probability.

=(Round your answer to 4 decimal places.)

B) What is the probability that daily production ismorethan 15.7 liters? Use technology (not tables) to get your probability.

=(Round your answer to 4 decimal places.)

10.A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5.4 years, and standard deviation of 1.5 years.

The 9% of items with the shortest lifespan will last less than how many years? answer to one decimal place.

11.A particular fruit's weights are normally distributed, with a mean of 398 grams and a standard deviation of 24 grams.

The heaviest 20% of fruits weigh more than how many grams? answer to the nearest gram.

12.Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.2-in and a standard deviation of 1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 1.8% or largest 1.8%.

What is the minimum head breadth that will fit the clientele?

min =

What is the maximum head breadth that will fit the clientele?

max =

answer as a number accurate to 1 decimal place. Answers obtained using exactz-scores orz-scores rounded to 3 decimal places are accepted.

13.The lengths of pregnancies in a small rural village are normally distributed with a mean of 270 days and a standard deviation of 17 days.

What percentage of pregnancies last fewer than 296 days?

P(X< 296 days) =%

answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exactz-scores orz-scores rounded to 3 decimal places are accepted.