statistic probability

3. A particular fruit's weights are normally distributed, with a mean of 223 grams and a standard deviation of 8 grams.

If you pick one fruit at random, what is the probability that it will weigh between 219 grams and 234 grams? Round to 4 decimal places.

4. A particular fruit's weights are normally distributed, with a mean of 433 grams and a standard deviation of 23 grams.

5. The heaviest 17% of fruits weigh more than how many grams? Round to 4 decimal places.

The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 36 liters, and standard deviation of 8.4 liters. Round all answers to 4 decimal places.

a.  What is the probability that daily production is less than 22.5 liters? First find the z-score.

     z =

    P( x < 22.5) =

b.  What is the probability that daily production is more than 40.9 liters? First find the z-score.

     z =

     P(x > 40.9)=

6. A distribution of values is normal with a mean of 69 and a standard deviation of 88.4.

Find P29, which is the score separating the bottom 29% from the top 71%.
P29 =

Enter your answer as a number accurate to 4 decimal places. 

8.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 6.5-in and a standard deviation of 0.9-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 0.5% or largest 0.5%.

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

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

Enter your answer as a number accurate to 4 decimal places.