1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
777dan777 [17]
2 years ago
13

Thefirstassignmentinastatisticalcomputingclass involves running a short program. If past experience indicates that 40% of all st

udents will make no programming errors, compute the (approximate) probability that in a class of 50 students a. At least 25 will make no errors [Hint: Normal approximation to the binomial] b. Between 15 and 25 (inclusive) will make no errors
Mathematics
1 answer:
Akimi4 [234]2 years ago
4 0

Answer:

(a) P(X \geq 25) = 0.0985

(b) P(15 \leq X \leq 25) = 0.8836

Step-by-step explanation:

We are given that past experience indicates that 40% of all students will make no programming errors. Also, a sample of class of 50 students is given.

Firstly, the above situation can be represented through binomial distribution, i.e.;

P(X=r) = \binom{n}{r} p^{r} (1-p)^{2} ;x=0,1,2,3,....

where, n = number of samples taken = 50

           r = number of success

           p = probability of success, i.e. 40%

Now, we can't calculate the required probability using binomial distribution because here n is very large(n > 30), so we will convert this distribution into normal distribution using continuity correction.

So, Let X = No. of making no programming errors

Mean of X, \mu = n \times p = 50 \times 0.40 = 20

Standard deviation of X, \sigma = \sqrt{np(1-p)} = \sqrt{50 \times 0.40 \times (1-0.40)} = 3.5

So, X ~ N(\mu = 20, \sigma^{2} = 3.5^{2})

Now, the z score probability distribution is given by;

                 Z = \frac{X-\mu}{\sigma} ~ N(0,1)

(a) Probability that in a class of 50 students at least 25 will make no errors is given by = P(X \geq 25) = P(X > 24.5)  ---- using continuity correction

   P(X > 24.5) = P( \frac{X-\mu}{\sigma} > \frac{24.5-20}{3.5} ) = P(Z > 1.29) = 1 - P(Z \leq 1.29)

                                                     = 1 - 0.90147 = 0.0985

(b) Probability that in a class of 50 students between 15 and 25 (inclusive) will make no errors = P(15 \leq X \leq 25) = P(X \leq 25) - P(X < 15)

P(X \leq 25) = P(X < 25.5) = P( \frac{X-\mu}{\sigma} < \frac{25.5-20}{3.5} ) = P(Z < 1.57) = 0.94179

P(X < 15) = P(X < 14.5) = P( \frac{X-\mu}{\sigma} < \frac{14.5-20}{3.5} ) = P(Z < -1.57) = 1 - P(Z \leq 1.57)

                                                                   = 1 - 0.94179  = 0.05821

Therefore, P(15 \leq X \leq 25) = 0.94179 - 0.05821 = 0.8836 .

                                                   

You might be interested in
I don't get this I really need help to understand this "/
Alisiya [41]
I don't either it is quite hard to be fair
4 0
3 years ago
Equivalent of -3(5+x)+4x
Natasha_Volkova [10]

Answer:

-15 + x

Step-by-step explanation:

5 0
3 years ago
A car averaged 48 miles per hour traveling 672 miles from Washington to Orlando. How long was the trip?
lora16 [44]
14 hours
672 miles / 48 mph = 14 hours total

4 0
3 years ago
Read 2 more answers
4. Find an equation for each line.
DedPeter [7]

Answer:

1 lap in 8/10 (4/5) of a minute

Answer is B, 8/10 minute!

⭐ Please consider brainliest! ⭐

✉️ If any further questions, inbox me! ✉️

Step-by-step explanation:

3 0
2 years ago
Suppose you roll a six sided number cube one time. What is the probability of rolling a 3 or an even number
Vikki [24]
There are 3 even numbers: 2,4,6. If you add 3 there is 4. There is 6 possible outcomes 1,2,3,4,5,6. So the probability is 4/6, 2/3, 66.666....% or 0.6666666....
8 0
3 years ago
Other questions:
  • Wyatt uses 3.15 cups of flour in a recipe that makes 9 shortcakes. Cora uses 2.4 cups of flour in a recipe that makes 8 shortcak
    15·1 answer
  • For the function y = 3x^2 - 12x + 4, what is the mirror point for the y-intercept? Give your answer in (x,y) point form.
    11·1 answer
  • Find 3 ordered pairs which are Solutions to the equation 2x - 3y = 12
    12·1 answer
  • 42 less than the product of 28 and an unknown number is 154 what is the value of the unknown number
    15·2 answers
  • Sherri borrowed $3,200 at 13 percent APR for 18 months. If she must pay 19.5 per $100, what is the total interest? $624 $3,824 $
    11·2 answers
  • A field has 25 trees in it . 14 trees are new and the rest are old . How many trees are old ? Write two different equations that
    15·1 answer
  • Plz help I need help
    12·1 answer
  • Pls pls pls pls pls pls pls
    13·1 answer
  • In circle G with m \angle FGH= 42m∠FGH=42 and FG=6FG=6 units find area of sector FGH. Round to the nearest hundredth.
    11·1 answer
  • A box is to be constructed with a rectangular base and a height of h cm. the length, l, of the box is 10 cm, and the width, w, i
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!