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Chapter 6: Q. 90 (page 405)

90. Normal approximation To use a Normal distribution to approximate binomial probabilities, why do we require that both np and n(1−p) be at least 10?

Short Answer

Expert verified

Both npand n(1-p) have different shapes, if the provided condition is not valid.

Step by step solution

01

Given information

Determine the Normal distribution to approximate binomial probabilities, does require for both npand n(1−p)be at least 10.

02

Explanation

If both np and n(1-p) are fewer than 10, the binomial distribution will not have the same approximate shape as the normal distribution. As a result, the binomial distribution cannot be approximated using the normal distribution.

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Most popular questions from this chapter

86.1in 6wins As a special promotion for its 20-ounce bottles of soda, a soft drink company printed a message on the inside of each cap. Some of the caps said, “Please try again,” while others said, “You’re a winner!” The company advertised the promotion with the slogan “1in6wins a prize.” Suppose the company is telling the truth and that every 20-ounce
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(c) The store clerk is surprised when three of the friends win a prize. Is this group of friends just lucky, or is the company’s 1-in-6 claim inaccurate? Compute P(X≥3) and use the result to justify your answer.

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(b) What outcomes make up the event B? What is P(B)?

(c) What outcomes make up the event “A or B”? What is P(A or B)? Why is this probability not equal to P(A) + P(B)?

North Carolina State University posts the grade distributions for its courses online.3Students in Statistics 101in a recent semester received 26%A42%Bs,20%Cs,10%Ds,and2%Fs. Choose a Statistics 101student at random. The student’s grade on a four-point scale (with A=4) is a discrete random variable Xwith this probability distribution:

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