Question

In: Statistics and Probability

Find the probability (approximate) in the following cases: a) Of 1000 random digits, 7 does not...

Find the probability (approximate) in the following cases:
a) Of 1000 random digits, 7 does not appear more than 968 times
b) Rolling 12000 a die, the number of six is between 1900 and 2150.
c) In 182 days, the number of units demanded of a certain product exceeds 6370 units (Note: the daily demand of the product has average 30 and standard deviation 6, and the independence of the demand of each day is assumed with respect to the rest)

Expert Solution

a) The probability of occurrence of digit 7 is . The number of occurrence of digit 7 out of 1000 is Binomial with . We use normal approximation to Binomial. The probability that of

1000 random digits, 7 does not appear more than 968 times is

b) The probability of occurrence of 6 is . The number of occurrence of 6 out of 12,000 is Binomial with . We use normal approximation to Binomial. The probability that

the number of six is between 1900 and 2150 is

c) In this part its is clear what probability is need to be calculated.

The average demand for 182 days is . The standard deviation of the demand for 182 days is

The probability that the number of units demanded of a certain product exceeds 6370 units is

Check the numerical values you have provided.

orchestra answered 2 years ago

a code is 4 random letters and 3 random digits. what is the probability of the...

a code is 4 random letters and 3 random digits. what is the probability of the 4 letters all being different while the 3. numbers at the end are in ascending order? b) in a group of 10 codes.... what is the probability that at least two have all different letters and numbers in ascending order c) in 1000 codes what is the wxpected value and standard deviation for the codes with all different letters and ascending digits

A fair coin is tossed 1000 times. Use the Central Limit Theorem to approximate the probability...

A fair coin is tossed 1000 times. Use the Central Limit Theorem to approximate the probability that between 470 and 530 heads are obtained. How does this compare to Chebyshev’s bound?

What are the approximate probabilities for the following situations for a random sample of 1000 individuals who have purchased fries at McDonald's?

In response to concerns about nutritional contents of fast foods, McDonald's has announced that it will use a new cooking oil for its french fries that will decrease substantially trans fatty acid levels and increase the amount of more beneficial polyunsaturated fat. The company claims that 97 out of 100 people cannot detect a difference in taste between the new and old oils. Assuming that this figure is correct (as a long-run proportion), what are the approximate probabilities for the...

Using the normal approximation, find the approximate probability of at most 16 successes of 40. You...

Using the normal approximation, find the approximate probability of at most 16 successes of 40. You may need to consult your z table or the shiny app

Find the following probability for a standard normal random variable, P(Z ≥ -2.16 )

A swedish license plate consists of three letters followed by three digits. Find the probability that...

A swedish license plate consists of three letters followed by three digits. Find the probability that a randomly selected plate has a) no duplicate letters b) no duplicate digits c) all letters the same d) only odd digits e) no duplicate letters and all digits equal

Find the probability of rolling a sum of two dice that is a 7 or a...

Find the probability of rolling a sum of two dice that is a 7 or a 12. Round answer to 4 decimal places.

2. Find the value of ? in the following cases: a. ?(−? ≤ ? ≤ ?)...

2. Find the value of ? in the following cases: a. ?(−? ≤ ? ≤ ?) = 0.6840 b. ?(? ≤ ? ≤ 1.40) = .8240 c. ?(−1.20 ≤ ? ≤ ?) = .5860

1. Use the 68-95-99.7 Rule to approximate the probability rather than using technology to find the...

1. Use the 68-95-99.7 Rule to approximate the probability rather than using technology to find the values more precisely. The daily closing price of a stock (in $) is well modeled by a Normal model with mean $158.14 and standard deviation $4.64. According to this model, what cutoff value(s) of price would separate the following percentage? a) highest 0.15% b) highest 50% c) middle 95% d) highest 2.5% 2. In the last quarter of 2007, a group of 64...

A coin will be tossed 7 times. Find the probability that there will be exactly 2...

A coin will be tossed 7 times. Find the probability that there will be exactly 2 heads among the first 4 tosses, and exactly 2 heads among the last 3 tosses. (Include 2 digits after the decimal point.)