A package of 6 bulbs are tested where the probability of an individual bulb is defective is 0.05. (That is, 5% of all the bulbs manufactured are defective). 1. Find the expected value of this. 2. Find the standard deviation of this distribution?

Americans receive an average of 20 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 7. Let X be the number of Christmas cards received by a randomly selected American. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N 20 ✓,7 b. If an American is randomly chosen, find the probability that this American will receive no more than 23 Christmas cards this year. c. If an American is randomly chosen, find the probability that this American will receive between 21 and 25 Christmas cards this year. d. 70% of all Americans receive at most how many Christmas cards? (Please enter a whole number)

The percent of fat calories that a person consumes each day is normally distributed with a mean of about 35 and a standard deviation of about ten. Suppose that 9 individuals are randomly chosen. Let X = average percent of fat calories. For the group of 9, find the probability that the average percent of fat calories consumed is more than six. (Round your answer to four decimal places.)

The average amount of money spent for lunch per person in the college cafeteria is $5.99 and the standard deviation is $2.1. Suppose that 49 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible. For the group of 49 patrons, find the probability that the average lunch cost is between $5.77 and $6.08.

The lengths of pregnancies are normally distributed with a mean of 268days and a standard deviation of 15 days. a. Find the probability of a pregnancy lasting 309 days or longer. b. If the length of pregnancy is in the lowest 2​%, then the baby is premature. Find the length that separates premature babies from those who are not premature.   a. The probability that a pregnancy will last 309 days or longer is   ​(Round to four decimal places as​ needed.)   b. Babies who are born on or before____days are considered premature. ​   (Round to the nearest integer as​ needed.)

Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.32 feet and a standard deviation of 0.40 feet. A sample of 83 men’s step lengths is taken.   Step 1 of 2 :   Find the probability that an individual man’s step length is less than 2.1 feet. Round your answer to 4 decimal places, if necessary.

The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 67 minutes and a standard deviation of 16 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible.b. Find the probability that a randomly selected person at the hot springs stays longer then 77 minutes. c. The park service is considering offering a discount for the 4% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount?  minutes.d. Find the Inter Quartile Range (IQR) for time spent at the hot springs.Q1: (.        ) minutesQ3: (         )minutesIQR:(         )minutes PLEASE ANSWER ALL 3 SUBS B, C, AND D

The average American man consumes 9.5 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.8 grams. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that this American man consumes between 9.2 and 10.1 grams of sodium per day. c. The middle 20% of American men consume between what two weights of sodium? Low: High:

The average THC content of marijuana sold on the street is 9.4%. Suppose the THC content is normally distributed with standard deviation of 2%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 7.9. Round to 4 decimal places. c. Find the 65th percentile for this distribution. Round to 2 decimal places.