1)A population of values has a normal distribution with mean=33.3 and standard deviation=32 , you intend to draw a random sample of size n=180.

a)find the probability that a single randomly selected value is between 36.9 and 40

P(36.9 < X < 40 )=

b)find the probability that a sample of size n=180 is randomly selected with a mean between 36.9 and 40

P(36.9 < M < 40 )=

Enter answers as numbers accurate to four decimal places, answers obtained using exact z-scores or z-scores rounded to three decimal places are accepted

2)A population of values has a normal distribution with mean=84.1 and standard deviation=76.6 , you intend to draw a random sample of size n=100

a)find P37, which is the score separating the bottom 37% scores from the top 63% scores. P37( for single values)=

b)find P37,which is the mean separating the bottom 37% means from the top 63% means. P(for sample means)=

Enter your answers as numbers accurate to 1 decimal place, answers obtained using exact z-scores or z-scores rounded to three decimal places are accepted.

3)A population of values has a normal distribution with mean=203.6 and a standard deviation=35.5 , you intend to draw a random sample of size n=52

Find the probability that a sample of size n=52 is randomly selected with a mean greater than 218.9

P(M > 218.9)=

Enter answer as numbers accurate to four decimal places,answers obtained using exact z-scores or z-scores rounded to three decimal places are accepted

4)A population of values has a normal distribution with mean=143.6 and standard deviation=4 , you intend to draw a random sample of size n=145.

Find the probability that a sample of size n=145 is randomly selected with a mean between 142.8 and 143.6

P(142.8 < M < 143.6)=

Enter the answers as numbers accurate to four decimal places, answers obtained using exact z-scores or z-scores rounded to three decimal places are accepted.

5)A population of values has a normal distribution with mean=34.1 and a standard deviation=69.7 , you intend to draw a random sample of size n=97

Find P88,which is the mean separating the bottom 88% means from the top 12% means. P88(for sample means)=

Enter your answers as numbers accurate to one decimal place, answers obtained using exact z-scores or z-scores rounded to three decimal places are accepted

6)A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 263.2-cm and a standard deviation of 0.6-cm. For shipment, 5 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is less than 263-cm. P(M < 263-cm)=

Enter your answer as a number accurate to four decimal places, answers obtained using exact z-scores or z-scores rounded to three decimal places are accepted.

7)A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 103.3-cm and a standard deviation of 1.6-cm. For shipment, 18 steel rods are bundled together.

Find P40, which is the average length separating the smallest 40% bundles from the largest 60% bundles. P40=

Enter your answer as a number accurate to two decimal places, answers obtained using exact z-scores or z-scores rounded to three decimal places are accepted.

8)A distribution of values is normal with a mean of 210 and a standard deviation of 15. From this distribution, you are drawing samples of size 40

Find the interval containing the middle-most 92% of sample means:

Enter your answer using interval notation. In this context, either inclusive or exclusive intervals would be acceptable. Your numbers should be accurate to one decimal places. Answers obtained using exact z-scores or z-scores rounded to three decimal places are accepted.