Question

Use the appropriate normal distribution to approximate the resulting binomial distributions. A convenience store owner claims that 55% of the people buying from her store, on a certain day of the week, buy coffee during their visit. A random sample of 35 customers is made. If the store owner's claim is correct, what is the probability that fewer than 20 customers in the sample buy coffee during their visit on that certain day of the week?

a) 0.4681

b) 0.6293

c) 0.5319

d) 0.5675

e) 0.5987

f) None of the above.

Answer 1

Solution :

Using binomial distribution,

= n * p = 35 * 0.55 = 19.25

= n * p * q = 35 * 0.55 * 0.45 = 2.9432

Using continuity correction ,

= P((x - ) / < (19.5 - 19.25) / 2.9432)

= P(z < 0.08)

= 0.5319

Probability = 0.5319

c)