A large national study finds that 10% of pregnant women deliver prematurely. A local obstetrician is seeing 16 pregnant women in his next clinic session. a.What is the probability that none will deliver prematurely? b.What is the probability that fewer than 3 will deliver prematurely? c.What is the probability that none will deliver prematurely if, in fact, the true percentage who deliver prematurely is 5.5%?

Question

A large national study finds that 10% of pregnant women deliver prematurely. A local obstetrician is seeing 16 pregnant women in his next clinic session.   a.What is the probability that none will deliver prematurely?   b.What is the probability that fewer than 3 will deliver prematurely?   c.What is the probability that none will deliver prematurely if, in fact, the true percentage who deliver prematurely is 5.5%?

jackbranv5 · Accepted Answer

Step 1 Given: - Probability of women deliver prematurely is, p=10%=0.1. - Number of pregnant women is, n=16. The objective is, a) To find the probability of none will deliver prematurely. b) To find the probability of fewer than 3 will prematurely. c) To find the probability that none will deliver prematurely if, in fact the true percentage who deliver prematurely is 5.5%. Step 2 a) The probability of none will be calculated as, x=0. P(X=0)=nCx⋅px⋅(1−p)n−x =16C0⋅0.10⋅(1−0.1)16−0 =(0.9)16 =0.185 Hence, the probability of none will deliver prematurely is 0.185. b) The probability of fewer than 3 can be calculated as, P(X&amp;lt;3)=P(X=0)+P(X=1)+P(X=2) =16C0⋅0.10⋅(1−0.1)16−0+16C1⋅(1−0.1)16−1+16C2⋅0.12⋅(1−0.1)16−2 =0.185+16⋅0.1⋅(0.9)15+16!(16−2)!2!⋅0.01⋅(0.9)14 =0.789 Hence, the probability of fewer than 3 will prematurely is 0.789. Step 3 c) To find the probability of none, if the percentage of premature delivery is, p=5.5%=0.055. P(X=0)=nCx⋅px⋅(1−p)n−x =16C0⋅0.0550⋅(1−0.055)16−0 =(0.945)16 =0.404 Hence, the probability that none will deliver prematurely if, in fact the true percentage who deliver premature is 5.5% is 0.404.

Nick Camelot · Accepted Answer

Step 1: Let&#039;s assume the measure of the angle is x.According to the problem statement, the measure of an angle is 6 less than 5 times its complement. The complement of an angle is the angle that, when added to the given angle, results in a right angle (90 degrees). The complement of x can be represented as 90−x.Given that the measure of the angle is 6 less than 5 times its complement, we can write the equation as:x=5(90−x)−6To solve this equation, let&#039;s simplify it:x=450−5x−6Step 2: Now, let&#039;s gather like terms:x+5x=450−66x=444To isolate x, we divide both sides of the equation by 6:6x6=4446x=74Therefore, the measure of the angle is 74 degrees.Step 3: To find the measure of the complement, we substitute x back into the expression for the complement:Complement =90−x=90−74=16Hence, the measure of the complement is 16 degrees.To summarize, the measure of the angle is 74 degrees, and the measure of its complement is 16 degrees.

Eliza Beth13 · Accepted Answer

Answer:x+65Explanation:According to the given information, we have the equation:x=5y−6To find the measure of the complement, we need to solve for y. Rearranging the equation, we get:5y=x+6Dividing both sides by 5, we have:y=x+65Therefore, the measure of the complement is x+65.

Mr Solver · Accepted Answer

According to the problem, we can set up the following equation:x=5(90∘−x)−6To solve this equation, we&#039;ll start by distributing the 5:x=450∘−5x−6Next, we&#039;ll combine like terms:x+5x=450∘−66x=444∘Finally, we&#039;ll solve for x by dividing both sides of the equation by 6:x=444∘6x=74∘Therefore, the measure of the angle is 74∘.To find the measure of its complement, we substitute the value of x back into the equation for the complement:Complement =90∘−x=90∘−74∘Complement =16∘Hence, the measure of the complement is 16∘.

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